Wells began his career in his native Bermuda, playing for Dandy Town Hornets and Bermuda Hogges. After moving to England, where he had a brief spell in non-league football with Eccleshill United, Wells has since played in the Football League for Carlisle United, Bradford City and Huddersfield Town.
Wells was born in Hamilton. He began his career in his native Bermuda with the Dandy Town Hornets, a team he had first joined at the age of 12. Wells had a trial with Dutch club Ajax as a teenager; he was offered a contract but ultimately did not sign for the club. After spending the 2009–10 season with the senior team of the Dandy Town Hornets, scoring 20 goals, Wells spent the 2010 season in the USL PDL with the Bermuda Hogges, scoring 2 goals in 9 games.
Wells later moved to England to attend the Richmond International Academic & Soccer Academy in Leeds, and also played club football with local non-League team Eccleshill United. Wells underwent a trial with Carlisle United in November 2010, his second with the club. Before moving to the UK, Well has sought the advice of compatriot Shaun Goater. In December 2010, it was announced that Wells would sign for Carlisle United on 1 January 2011. Wells made his debut for Carlisle United on 15 January 2011, in a League One game against Bristol Rovers. In March 2011, Wells publicly announced his wish to play at Wembley Stadium with Carlisle United in the 2011 Football League Trophy Final, to be played in April 2011. However, Wells did not make the matchday squad, as Carlisle United beat Brentford 1–0.
On 3 May 2011, it was announced that Wells' contract with Carlisle United would not be renewed at the end of the season.
In late June 2011, Wells went on trial with Bradford City alongside four other players. He signed a one-year contract with Bradford City on 22 July 2011. Wells made his debut for Bradford City on the opening day of the 2011–12 season, coming on as a 74th-minute substitute for Mark Stewart. He scored his first goal for the Bantams in a 4–2 win against Barnet.
On 9 March 2012, Bradford City exercised an option in Wells' contract, and extended his deal by one year. On 14 April, he scored a hat-trick as Bradford beat Northampton Town 3–1. He was later named in the Football League Two Team of the Week for that week. Following this, former Bradford City player Dean Windass urged Wells to remain with the club, while ex-Bermudian international Kyle Lightbourne compared him to Jermain Defoe. In early May, Wells and Bradford City began discussions over a new four-year contract, and later that month he publicly assured fans that he would stay with the club. In June there were further rumours of Wells leaving the club, while it was later revealed that he nearly never signed for the club in the first place. In July, Wells stated he was in no rush to sign a new contract.
Wells scored a penalty on the opening day of the 2012–13 season in an away match against Gillingham. He scored his second goal of the season on 25 August in a 5–1 win against AFC Wimbledon, and also assisted the fifth goal, crossing for James Hanson to score with a header. In September 2012, Wells suffered a hip injury. On 25 September, Wells came off the bench to score two late goals to help Bradford overturn a 2–0 deficit against Burton Albion in the League Cup third round, with Bradford going on to win the game 3–2 in extra time. At the end of September 2012, Wells signed a new three-year contract with the club, in a move praised by Phil Parkinson, the club's manager. In October 2012, Wells was banned by the club from celebrating his goals. As the January 2013 transfer window opened, Bradford City dismissed rumours linking Wells with a move away from the club. On 8 January 2013, he helped Bradford beat Premier League side Aston Villa 3–1 in the first leg of the semi-final of the League Cup by opening the scoring in the 19th minute. After appearing in the 2013 Football League Cup Final, Wells became the first player from Bermuda to appear in an English major cup final. Although Wells did not complete the game, prior to the match he spoke about being motivated by the recent death of a friend in a motorcycle accident, as well as how he was looking forward to facing opponents from a higher league. Wells hadn't scored for the club since 2 February 2013, until he scored the only goal of the game on 6 April 2013, in a 1–0 home victory against Northampton Town. Later that month, he was linked with a transfer to Burnley.
In May 2013, Wells scored three goals across two legs to help Bradford City qualify for the League Two play-off final. The goals took his tally for the season to 25, a target he had set himself before the season begun. He then scored in the final against Northampton Town, which Bradford won 3–0 to earn promotion to League One. Following the promotion, Wells stated he wished to stay at the club, though the club later admitted they might sell the player if a suitable offer came in. Former City player John Hendrie advised Wells to remain at the club.
Ahead of the 2013–14 season, Wells spoke of his desire for another good cup run, and his belief that the club could achieve a second successive promotion. In June 2012, manager Phil Parkinson said that only a high-money bid would persuade the club to sell either Wells or fellow striker James Hanson. In July 2013, the club rejected a bid from Peterborough United, and later revealed that they had had no further offers for the player. In August 2013, Wells' strike partner Hanson spoke positively of his partnership with Wells. On 24 August 2013, Wells scored two goals in a home match against Sheffield United; in the process he set a new club record by scoring in his eighth consecutive match, a feat which was praised by teammate James Hanson. After the match the club re-stated that they would not sell Wells, and later confirmed they had not received any bids for the player on transfer deadline day. On 4 September 2013, Wells was nominated for the League One Player of the Month award, winning the award two days later. Wells has publicly praised his strike partnership with Hanson, as has journalist Simon Parker, who described them as "[one of] the best front pairs that League One has to offer." Of the 53 goals that Wells scored for Bradford City, 49 came when he was playing with Hanson.
In late September 2013 Wells suffered ankle ligament damage in a match, and was ruled out for a number of weeks. Manager Phil Parkinson stated he would not rush Wells back into play, Wells returned, after two months out, to score a hat-trick against Coventry City. In December 2013, club co-chairman Julian Rhodes admitted that the player might leave the club, as rumours surrounding the player's possible departure began to increase. That same month, colleague Andrew Davies described Wells and Hanson as the best strike pair in the division, and Davies also urged Wells to remain with the club, while manager Phil Parkinson said that he did not want the club to sell the player. Wells picked up an injury at the end of December 2013, and at the start of the January 2014 transfer window, manager Phil Parkinson said he wanted any transfer issues sorted quickly. The next day, 3 January 2014, the club announced that they had already rejected one offer for the player, after saying that Wells has been receiving interest from a number of Premier League clubs, as well as Championship side Burnley. The club also said they would lose £1 million for the 2013–14 season if they did not sell Wells. Despite all the speculation, Parkinson said he felt Wells would be able to ignore off-the-field matters and concentrate on his playing, though he later admitted that the player was being affected by the rumours.
On 10 January 2014, Wells signed a four-and-a-half year contract with Huddersfield Town after transferring for an undisclosed club record fee. The deal was initially completed a one-game loan deal, to allow time for the paperwork for the permanent move to be completed. Wells was criticised by a section for moving from Bradford City to a team considered a rival. On 11 January 2014, Wells made his Huddersfield Town debut, appearing as a substitute in the 55th minute, and scoring the winning goal in a 1–0 home victory against Millwall, less than 24 hours after joining the club.
Wells ended his first full-season with Huddersfield Town as the club's top scorer with 14 goals. At the end of the 2016–17 season, former club Bradford City received a £250,000 bonus payment following Huddersfield's promotion to the Premier League.
Wells, in the final year of his contract with Huddersfield, signed a three year deal with Burnley for £5 million on 31 August 2017.
Wells made his international debut for Bermuda in 2007.
Wells also made four unofficial international appearances for Bermuda in the 2007 Island Games.
In late August 2011, Wells was recalled by Bermuda, joining their squad for FIFA World Cup qualifying matches in early September 2011. Wells appeared in five 2014 FIFA World Cup qualifying matches for Bermuda, against Barbados, Guyana and Trinidad and Tobago.
Wells was described as "one of Bermuda's most promising players, with an exceptionally bright future" in February 2012 by then Sports Minister Glenn Blakeney, and was honoured by Premier Craig Cannonier in June 2013. He has been described as the country's "star footballer".As of match played 31 August 2017.
As of match played 29 March 2015.
As of match played 29 March 2015. Scores and results list Bermuda's goal tally first.
Bradford CityFootball League Cup: runner-up 2012–13
Football League Two play-offs: 2012–13