He began his career in non-league football with St. Ives Town, joining Newport County for £5,000 in 2012. After helping them return to The Football League via the play-offs, he transferred to Peterborough United in January 2014. Two years later, he signed for Queens Park Rangers for an undisclosed fee.
Born in England, Washington qualified for Northern Ireland through a grandparent. He made his senior debut for the team in March 2016 and was chosen for that year's European Championship.
Born in Chatham, Kent, England, Washington was eligible to play for Scotland through his mother, and through a grandmother to play for Northern Ireland. After his parents moved to St Ives, Cambridgeshire during his childhood, he began to show his scoring capability by winning trophies as part of the Westfield Junior School squad. After graduating school, he was turned down for an apprenticeship by both Norwich City and Peterborough United. He subsequently worked as a postman for the Royal Mail, whilst developing his football as a striker for St. Ives Town, scoring 52 goals in 50 matches in the United Counties League, Premier Division.
Washington joined Newport County on 1 October 2012 for a fee of £5,000, after being spotted by their manager Justin Edinburgh. He made his debut 26 days later in a 3–2 home loss to Woking, replacing Ben Swallow for the final nine minutes. The only goal of his 15 appearances in his first season was the game's only on 9 April 2013 against Braintree Town at Rodney Parade. Newport finished 3rd in the Conference Premier and reached the play-offs, though he was not selected in the matchday squad for the playoff final which Newport won 2–0 against Wrexham at Wembley Stadium to return to the Football League after a 25-year absence.
Washington made his Football League debut in League Two versus Accrington Stanley on 3 August 2013, and his League Cup debut in the first round at Brighton & Hove Albion three days later, scoring the third goal in Newport's 3–1 win. His first Football League goal came on 10 August in County's 3–1 reverse at Northampton Town.
On 28 January 2014, Washington joined Peterborough United for an undisclosed fee, with Shaun Jeffers moving the other way as part of the deal. As part of the deal, Newport retained a 20% sell-on clause.
He made his debut for the Posh on 8 February, replacing Jack Payne for the final 17 minutes of a 2–1 win away to Leyton Orient. His first goal in League One came on 8 March, concluding a 4–2 victory over Crewe Alexandra at London Road; he assisted two further goals. Washington scored three more goals over the season, including two in a win of the same score at Shrewsbury Town on 26 April, and added another in the play-off semi-final defeat to Orient.
On 7 November 2015, Washington scored the first two goals of a 3–0 win away to Burton Albion in the first round of the FA Cup, and three weeks later he added his first professional hat-trick in a 4–0 victory at Scunthorpe United.
On 19 January 2016, Washington joined Queens Park Rangers on a three-and-a-half-year deal for an undisclosed fee that was reported to be between £2.5m and £3m. Four days later, he made his debut by replacing Junior Hoilett with seven minutes remaining in a 1–1 home draw against Wolverhampton Wanderers.
After failing to score a goal in his first season at Loftus Road, Washington scored his first goal for the club in extra time of a League Cup first round match at home to Swindon Town on 10 August 2016, putting his team 2–1 ahead. The game ended 2–2 and he scored in their 4–2 penalty shootout victory.
Gossip is that in the summer of 2017 Birmingham City want to buy Washington from Queens Park Rangers
Washington received his first call-up to the senior Northern Ireland squad on 16 March 2016 for friendlies against Wales and Slovenia; he had only been to the nation once, for a Peterborough friendly. He made his debut against Wales on the 24th, and four days later he scored his first goal, the only one against Slovenia at Windsor Park. In June 2016 Washington was named in the Northern Ireland squad for the UEFA Euro 2016 tournament. He scored his first competitive goal in Northern Ireland's 2–0 home World Cup Qualifying victory over Norway on 27 March 2017, making it three goals in three starts for him in the National Stadium.As of match played 18 March 2017
As of match played 26 March 2017.
As of match played 26 March 2017. Northern Ireland score listed first, score column indicates score after each Washington goal.