Watkins joined Exeter City's academy at U11 level, having previously failed a trial with the club at the age of 9 in 2003. He rose through the youth ranks to sign a scholarship deal in 2012 and off the back of scoring 30 goals for the U18 team in its 2013–14Football League Youth Alliance South West Conference-winning season, he signed a two-year professional contract in April 2014. Watkins won his maiden first team call up when he was named as a substitute for the final League Two match of the 2013–14 season versus Hartlepool United and he made his senior debut when he replaced Aaron Dawson after 77 minutes of the 2–0 victory. Watkins was frequently named as a substitute by Paul Tisdale during the first three months of the 2014–15 season, but despite scoring his first senior goal, he made just three appearances before departing on loan to Weston-super-Mare for the remainder of the campaign in December 2014.
Weston-super-Mare (2014–15)
On 8 December 2014, Watkins and Exeter City teammate Matt Jay joined Conference South club Weston-super-Mare on one-month loan deals. Through repeated extensions of the loan, Watkins would remain with the Seagulls until the end of the 2014–15 season. He featured regularly for the team, scoring 10 goals in 25 appearances before returning to St James Park at the end of the season.
Breakthrough (2015–2017)
After failing to be named in a first team squad during the opening two months of the 2015–16 season, Watkins broke onto the substitutes' bench in October 2015 and made his first appearance of the season late in the month. He made his first start for Exeter City in a 2–1 Devon derby victory over Plymouth Argyle on 6 December and scored his first goal of the season with the Grecians' second in a 2–0 FA Cup second round victory over Port Vale in the following match. By March 2016, Watkins had broken into the starting lineup. He had a fantastic month in March, scoring four goals in six appearances to win the Football League Young Player of the Month and PFA Fans' Player of the Month awards. His goalscoring run extended into mid-April and finished with eight goals in 10 appearances. Two of the goals came in the return Devon derby with Plymouth Argyle, in which his late brace sealed a 2–1 comeback victory and the second goal was subsequently voted as the club's Goal of the Season. Watkins finished the 2015–16 season with 10 goals in 22 appearances. Watkins' performances in the final two months of the 2015–16 season saw him enter 2016–17 as an established member of the first team squad. He had an eventful season, making 52 appearances, scoring six goals and contributing 13 assists, though the campaign ended on a sour note with the Grecians' 2–1 defeat to Blackpool in the 2017 League Two play-off Final at Wembley Stadium. Watkins scored the first hattrick of his career in a 4–1 win over Newport County on 31 December 2016 and his two goals and five assists in January 2017 saw him win the EFL League Two Player of the Month award. On 9 April he was award the EFL Young Player of the Year award for his performances during the season. Watkins left Exeter City on 18 July 2017, having made 78 appearances and scored 26 goals during three seasons as a professional at St James Park.
Brentford (2017)
On 18 July 2017, Watkins joined Championship club Brentford on a four-year contract, with an option for a further year, for an undisclosed fee, reported to be £1.8 million. He scored his first competitive goal for the club in their 3–1 EFL Cup first round extra time victory over AFC Wimbledon on 8 August 2017. On 9 August 2019 Watkins signed a new 4-year contract with a 1-year extension option. Watkins scored his first hat-trick for the club in their 3–1 Championship win against Barnsley F.C. in a 3–1 win on 29 September 2019.
Style of play
Watkins describes himself as "a number 10" and named Thierry Henry as his sporting idol, stating that "I try to base my game on his, by driving at defenders and looking to make something happen when I get the ball". He is also adept as an attacking midfielder or Winger. He was groomed as a centre forward during 2019.