After being overlooked in the National Draft, Betts was recruited to the AFL through the 2004 Pre-Season Draft by the Carlton Football Club with the No. 3 pick. He attracted attention as a lively small forward during the 2005 Pre-Season, and made his AFL debut in Round 1, 2005 against North Melbourne. His early performances saw him become a regular member of the senior team, filling the niche of goal-sneak and chaser for the club, while his sometimes freakish displays of skill saw him labelled an excitement machine by commentators.
Throughout his first four seasons, Betts had a consistent output of 20-25 goals as a small forward playing underneath full forward Brendan Fevola. In 2006, Betts won the Goal of the Year, for his goal in Round 21 against Collingwood; in an amazing solo effort, Betts smothered Tarkyn Lockyer's attempted clearing kick, ran to gather it just before it went out of bounds, and steadied himself to score with a banana from a seemingly impossible angle. From 2007, Betts began to spend some rotations as a midfielder, particularly late in the season after the appointment of Brett Ratten as Carlton coach, but remained primarily a small forward.
From 2009, Betts' goalkicking output increased. He kicked 38 goals in 2009, then 42 in 2010 to top Carlton's goal kicking for the first time. He played his 100th AFL game in Round 3, 2010 against Essendon at the MCG. His 2010 season saw him make the top 10 in the club Best and Fairest for the first time. Betts kicked another 50 goals in 2011, including a career-best eight goals against Essendon in Round 18, and then 48 goals in 2012 to be the club's leading goalkicker for the second time. He finished second in the best and fairest in 2012, narrowly beaten by Heath Scotland, and he was nominated in the 40-man All-Australian squad in both 2011 and 2012, but did not make the final team in either year.
The conclusion of the 2013 AFL season saw Betts enter the free agent market. On 3 October, Betts notified Carlton he has accepted a 4-year contract worth $2 million (AUS), to join Adelaide. Carlton had 72 hours to match the Crows offer but declined before that time elapsed, allowing the confirmation of Betts' switch to occur on 4 October.
In his first season at Adelaide, Betts played all 22 games and kicked a career-best 51 goals, leading Adelaide's goalscoring and finishing eighth in the Coleman Medal. He also had more goal assists than anyone else in the AFL and was ranked third in the league for tackles inside the forward 50. Betts played his 200th AFL game against Hawthorn at Adelaide Oval in round 17.
On May 26, 2015, the AFL launched an inquiry into Betts' signing with Adelaide after outgoing Carlton coach Mick Malthouse claimed to have been told by current Carlton and former Adelaide CEO Steven Trigg that Adelaide had illegally signed Betts 18 months prior to him departing Carlton. Adelaide categorically denied the claim, as did Carlton and Betts' manager. Betts and all other parties were subsequently cleared of any wrongdoing in the affair.
In December 2009, Betts was arrested and fined by police after being drunk in public following Carlton players' Christmas party. He was also fined and suspended for one month by the club for the incident. He and other players were sent to a boxing gym and underwent a strenuous training program. This in fact had a positive effect and they applied themselves so well that they achieved best ever levels of fitness (which had never been one of Eddie's strengths) and convinced the club that they had the right attitude.
He is married to Anna Scullie and together they have a son who was born in October 2012.