Watson was selected at pick 40 under the father–son rule in the 2002 national draft. He was initially coached as a key forward by Kevin Sheedy, who also coached his father, Tim Watson. His poor kicking by AFL standards drew criticism, and it was determined that he would be more suited to the midfield at Essendon. At the time, his weight was criticised by the media, as he was overweight for an AFL player. Over the next two seasons, he began to develop his craft in the Essendon midfield and became one of the competition's elite midfielders.
Watson had a consistent season in 2009, polling ten Brownlow Medal votes and winning the Essendon best-and-fairest award, the W. S. Crichton Medal. Watson polled 335 votes in 15 of the 21 games he played in the 2009 season, with only one game missed due to an ankle injury. Watson was 46 votes ahead of runner-up Dustin Fletcher, who polled 289 votes. By the end of the 2009 season, Watson had gathered a reputation as Essendon's most important midfielder (coming first in the club's overall clearances) and improved his once-criticised kicking ability to above the standard of an AFL player. Watson was announced as the captain of the Essendon Football Club on 21 December 2009, taking over from retired champion goalkicker Matthew Lloyd.
Despite Essendon suffering a disappointing 2010 season, winning only seven games and finishing 14th on the AFL ladder, Watson enjoyed a successful first year as captain. He was a consistent performer in an inconsistent season for the Bombers, polling 16 Brownlow votes from a total of only 43 received by Essendon players, finishing equal-seventh in the 2010 Brownlow Medal count, and having the highest number of votes for a player from a team finishing outside the final eight. Watson was once again awarded the Crichton Medal, earning 291 points, which was 50 points clear of runner-up Heath Hocking.
Watson had a relatively good season in 2011 despite missing six weeks with a hamstring injury, earning 15 Brownlow votes and finishing runner-up in the Crichton Medal, losing out to up-and-coming third-year midfielder David Zaharakis. Watson completed an outstanding 2012 season by winning his first Brownlow Medal with 30 votes. Along with his third Crichton Medal, he also won a handful of other accolades, including the AFLPA Best Captain Award, the Lou Richards Medal and a place in the All-Australian team for the first time. Watson missed three weeks with a broken collarbone in 2013, but had another consistent season, earning 17 Brownlow votes, finishing runner-up in the Crichton Medal to former St Kilda utility Brendon Goddard, and making the All-Australian team for the second time. Between 2006–2013, Watson finished all but one season in the top two for votes for the Crichton Medal.
Watson had a good start to the 2014 season, but injured his hip flexor in round 12 and consequently missed ten weeks. Watson later returned to play in the final three games of the home-and-away season and Essendon's elimination final loss to North Melbourne. Watson then went on to poll eight Brownlow votes, behind up-and-coming midfielder Dyson Heppell. Watson was also selected in the Australian team for the first time in his career to play in the 2014 international rules test. Watson was among the best players in the one-test series, which Australia won by ten points.
In 2015, despite controversy surrounding the team's lack of fitness (following a compromised pre-season) and a tough first half of the season for Essendon, Watson continued to lead his team well early in the season despite his own injury clouds, further enhancing his status as one of the game's best captains late in his career. In Round 14, Watson played his 200th AFL match in what proved to be a torrid day for the Bombers, as they lost to St Kilda by 110 points. Following that match, Watson was ruled out for the rest of the season with a shoulder injury, having injured it the previous week. Watson polled seven Brownlow votes in the first five rounds prior to the injury.
On 24 June 2013, whilst the Essendon Football Club was being investigated by the Australian Sports Anti-Doping Authority (ASADA) over the legality of its supplements program during the 2012 season, Watson admitted on the Fox Footy program On The Couch that he believed he was given the substance AOD-9604 during the 2012 season with the assistance of the club. The World Anti-Doping Agency (WADA) released a statement clarifying that AOD-9604 fell into the "S0. Non-Approved Substances" category in their List of Prohibited Substances and Methods. ASADA also stated that the use of AOD-9604 is prohibited for use by athletes in any circumstances. During the second phase of the investigation, Watson was among the thirty-four present and former Essendon players issued show cause notices by ASADA and infraction notices by the AFL, alleging the use of the banned peptide Thymosin beta-4 during the 2012 season.
On 31 March 2015 the AFL Anti-Doping Tribunal found all thirty-four players not guilty of all charges. In January 2016 following an appeal by WADA against the AFL Tribunal's not guilty finding, Watson, along with the other 33 players, had their not-guilty verdict overturned. All 34 players were suspended for two years, backdated to March 2015, ending in November 2016, meaning that he will miss the entire 2016 AFL season. Following the suspension, the AFL Commission announced that it would review the status of Watson's 2012 Brownlow Medal at a commission meeting in February 2016.