Adam was with Cambridge United since leaving Norwich City at the age of 13, making a youth team starting place his own as a schoolboy and retaining it ever since. He plays centre-half and right-back and made a handful of reserve team appearances in the 1998-99 season at the age of 16. He started 1999/2000 tremendously well by being selected for an England Under 18 training get-together, was then called up to the Under 18 squad for their friendly against Switzerland at the beginning of September, and signed a three year contract three days before making his international debut as a substitute. He was the first United player capped for England Under-18s since Dean Greygoose in 1983.

Roy McFarland, himself a respected former England defender, speaks highly of Adam and commented after his England Under-18 debut, "If he continues to make progress at this rate, it won't be too long before he'll be putting a bit of pressure on the older players. The thing about him is that, as well as centre-back, he could play at full-back, or even as a defensive midfielder."

'Tanny' continued his dream season with a call-up to the full 18-man squad which played three UEFA Under 18 Championship qualifiers in October, and featured in all three games. He came off the bench against Spain and Cyprus and started against San Marino.

Youth team manager Dale Brooks describes him thus: "He's fairly quick, he's got a decent range of passing ability - although that's something he obviously needs to work on - and he's a good all-round athlete. He's still in that development stage, but I'm sure he'll go on. He plays for me at centre-half, but I think it's good for a lad's development to play in different positions because it widens your opportunities," he said.

Adam was included in a couple of first team squads when they travelled and stayed overnight, and after one such trip, to Bristol City in November, he was named as a substitute for the first time. His first team debut came at the Abbey in January 2000 when he played at right-back in the first round AWS tie against Barnet, and he gave a composed performance and showed some good skill but was beaten for the extra time winner.
U's Net writer Will Jones watches many of the reserve games and says of Adam: "Adam Tann has the head of an experienced, cultured football player on the shoulders of a teenager. His slight frame offered little barrier to his progress from a highly successful youth team to reserve team action last season, and indeed barely put a foot wrong when faced with some quite daunting opposition strikers. Not afraid to get stuck in, spy a killer pass, or take the ball forward at his feet Adam is as close to the finished article as you can get at his age.
His favoured position is yet to be established, but whether it be right back, centre-back, left back or defensive midfield Adam has the range of skills that enable him to do a decent job. I would hope, however, that he could settle on one position and use the next year to develop that and prepare himself for the hard transition to first team football. I have no doubt whatsoever that he will play in the first team at United and be a complete success.
"The next year is a critical stage in his career though, but with his feet remaining secured to the ground - despite the rare accolade of a second divison youth player representing England at his level - he will have few problems. A young player to be looked after, nurtured and developed in the same mould as the other products of the youth system; asking too much of him too early could hamper his development into the great player he will be."

In March 2001, Adam joined local rivals Cambridge City on loan in order to get much needed match practice.

Tann left Cambridge United following their relegation to the Conference in May 2005. He joined Reading on trial in July 2005. Although he returned to Cambridge on trial, he joined Ipswich for training in mid-August 2005. After a trial with Rushden and Diamond, he signed for Gravesend at the end of October 2005. By the beginning of November, he had moved again joining Notts County for whom he made his debut against Bristol City on 5th November 2005, scoring County's opener in their 2-0 FA Cup First Round victory.

Adam switched to Leyton Orient on 18th January 2006. After their promotion to League One, Adam was offered a new one-year deal which he signed on 26th May 2006. Testing positive for testicular cancer, Adam underwent treatment in October 2006.

Adam turned down an offer of a new contract from Orient in May 2007 and signed instead for Notts County

In July 2009, Adam trialled with Conference side Histon, playing in their pre-season friendly against West Bromwich Albion. This became permanent

Despite being offered a coaching role at Histon and having made 39 appearances for Histon in 2009-10, Tann joined Chelmsford City on 20th July 2010

During the 2012/13 season, Tann had a loan spell at Bury Town.

On 4th December 2013, Tann was appointed First Team Coach at Ryman League side Leiston, working under new manager Steve Ball.

In January 2015, he moved to Southern League side St Neots Town.

He joined AFC Sudbury in June 2016. Manager Jamie Godbold said "I am really pleased to have secured someone as experienced as Adam. He knows that he is coming towards the end of his career, so he just wants to his enjoy his football and that suits us. [Adam] has played hundreds of games at very good levels and that is a big plus. He will be a calming influence both on and off the pitch, which we are going to need in a league where a lot of players have never played before"

Tann decided to retire in the summer of 2017 following Sudbury's relegation.

By the start of the 2018/19 season, he was registered with Lowesfoft. He then became player-coach.

Lowestoft were relegated from the Southern League Premier Central Division in April 2022.

Tann is the cousin of Ryan and Rossi Jarvis.