Adeyemi started his professional career at Football League Championship side Norwich City in 2008, having progressed through the club's youth ranks, and made his professional debut for the club in 2009. During his five-year spell at the club as a professional, he made eleven league appearances. He spent the 2010–11 season on loan to Football League Two side Bradford City, where he made 34 league appearances, and the next season on loan to Oldham Athletic of Football League One, making 36 league appearances. He was sent out on loan again for 2012–13, this time to League One Brentford, where he made 30 league appearances.
He joined Football League Championship club Birmingham City in July 2013 on a free transfer, having been released by Norwich, and a year later moved again, to fellow Championship club Cardiff City.
Adeyemi, a Tottenham Hotspur supporter, attended Norwich School and, having worked his way through the club's youth structure, signed professional forms for Norwich aged 17, in November 2008. He opted to decline a university offer from Cambridge University to pursue his footballing career, subsequently gaining A* grades at Advanced Level in Biology and Chemistry and an A grade in Mathematics.
Adeyemi made his debut for Norwich's first team on 8 August 2009, as a substitute for Matthew Gill during their heavy 7–1 defeat to Colchester United on the opening day of the 2009–10 season.
Former manager Glenn Roeder, who gave him his professional contract, described him:
"He's very athletic, technically very gifted and one of the nicest young men that I've ever dealt with. He comes from a lovely family, and academically he's incredibly intelligent – I don't think he got anything less than an A grade in his GCSEs. My son goes to the same school and the headmaster told me if Tom decides at any point he doesn't want to play football he can go back to Norwich School, get his A levels and end up at Oxford or Cambridge, and I don't think he means their football teams!"
In March 2010, Adeyemi was named League One Apprentice of the Year at the Football League Awards.
In July 2010, following Norwich City's promotion to the Championship, Adeyemi joined League Two side Bradford City on an initial six-month loan deal, later extended to a full season loan. He scored on his debut in a 3–1 loss against Shrewsbury Town.
Adeyemi signed for League One side Oldham Athletic on a five-month loan deal in August 2011. Adeyemi made his debut for the club in a 1–1 draw with local rivals Huddersfield Town. Adeyemi scored his second goal for the club against Carlisle United after getting his debut goal against Milton Keynes Dons in the televised 2–1 win. During Oldham's FA Cup third round tie against Liverpool at Anfield, Adeyemi thought he was the target of racist abuse from an individual in the stands, which led to a police investigation. An arrest was made, but the Crown Prosecution Service found "insufficient evidence to bring any criminal charges".
On 11 April 2012, at the end of Adeyemi's loan deal, Oldham decided not to extend his deal until the end of the season and allowed him to return to parent club Norwich City. Adeyemi made 45 appearances and scored three goals.
He joined League One Brentford on a six-month loan deal on 29 August 2012, signed by Uwe Rösler. Adeyemi impressed in the centre of midfield and extended his loan until the end of the season. He played in the dramatic final match of the regular season, against Doncaster Rovers, in which Brentford's Marcello Trotta missed a last-minute penalty which would have earned Brentford automatic promotion, only for Doncaster to run up to the opposite end of the pitch and score a winner. Brentford entered the play-offs, in which they beat Swindon Town in the semi-final only for Adeyemi to be on the losing side in the final, beaten 2–1 by Yeovil Town.
On 24 June 2013, following his release from Norwich City, Adeyemi signed a two-year contract with Championship club Birmingham City. Manager Lee Clark described him as "a terrific young lad who is a powerful and athletic midfield player who can get forward and score goals." He made his debut in a 1–0 defeat at home to Watford on 3 August, and remained a regular member of the starting eleven. He scored the winning penalty, albeit off the crossbar and the goalkeeper's back, to defeat Yeovil Town in the second round of the League Cup, and scored his first goal in the third round as Birmingham beat holders Swansea City 3–1. He stole the ball on the edge of Swansea's penalty area and knocked it to Chris Burke; Burke's return pass left Adeyemi a tap-in.
In the latter part of 2013, Birmingham went ten games unbeaten with a team built around a "spine" of Adeyemi and loanees Kyle Bartley, Dan Burn and Jesse Lingard, but the loanees were recalled, Adeyemi suffered a back injury which appeared to restrict his physicality when he was fit to play, and the team struggled. He was able to produce a strong performance on the final day of the season, when Birmingham avoided relegation on goal difference, was chosen as the club's young player of the season, and felt that increasing maturity was allowing him to take on more responsibility. Ahead of the 2014–15 season, Clark appointed Adeyemi vice-captain. Ten days later, amid interest from Cardiff City, he submitted a transfer request. Birmingham manager called losing Adeyemi "gutting".
Adeyemi signed a three-year contract with Championship club Cardiff City, managed by Ole Gunnar Solskjær, on 7 August 2014. The fee was undisclosed, but reported in the Birmingham Mail as "in excess of £1 million, with add-ons [and] a sell-on clause".
On 26 December, Adeyemi scored his first goal for Cardiff with a header that earned his side a point in a 1–1 draw with Charlton Athletic. On 20 January 2015, he received the man of the match award in a 2–1 defeat against Middlesbrough.
On 14 July 2015, Adeyemi joined Championship rivals Leeds United on a season-long loan with the option of a permanent deal, which would potentially be worth £1m. The move to Leeds saw Adeyemi link up with his former Brentford manager Uwe Rösler. Adeyemi made his debut for Leeds in a 1–1 draw with Burnley on the opening day of the season. On 29 August, Adeyemi scored his first competitive goal for Leeds with a bullet header in the first half of the 2–1 win over Derby County.
On 18 August 2016, Adeyemi joined Rotherham United on a season-long loan.
Adeyemi moved to Ipswich on 30 June 2017.
The son of a Nigerian father, Adeyemi is eligible for both the Nigeria and England national sides.
Adeyemi was described by Birmingham manager Lee Clark as a "powerful and talented midfielder". Rösler assessed him as composed. Solskjær expected him to be "a top, top player" for Cardiff, as "a box to box midfielder [who] can attack and defend. He wins the ball really well for us, switches the play and scores goals as well".As of match played 7 May 2017
Football League One: 2009–10
Football League One play-offs: runner-up 2012–13
Birmingham City Young Player of the Year: 2013–14
Football League One Apprentice of the Year: 2009–10