Watson began his motor racing career at the age of 15, in the Ginetta Junior Ireland Championship, making regular podiums through to 2011. That year, Andrew joined Douglas Motorsport team to race in the final two rounds of the Ginetta Junior Championship at Silverstone.
2012 saw Watson contest the entire Ginetta Junior championship season, again with Douglas Motorsport. The season saw him deliver fifth place in the Championship, achieving six podium places, including second places and his maiden victory, with only two non-finishes out of the twenty-round season.
At the first meeting of the season at Brands Hatch Indy circuit, Watson qualified second despite having little experience in the much more powerful G55 car. This translated to a seventh-place finish in round 1, followed by an eighth place in round 2, both on the Saturday. Round 3 was held on Sunday an even more impressive finish in fourth place cemented his arrival in the senior ranks.
Success at Donington Park at the second meeting of the year, was not so easy to repeat but Watson did qualify 3rd and managed to get the fastest lap in round 5.
Watson achieved his first podium in the GT Supercup, with a second-place finish in round 7, at the year's third meeting at Thruxton in Hampshire.
At Knockhill, Watson achieved pole position for round 18 (being the meeting's 1st race) on 24 August. This could not be converted to a maiden race win in the GT Supercup owing to him having to serve a drive-through penalty. He eventually finished the race in 10th place.
In round 20 at Knockhill, Watson led the race for 23 of the 24 lap race however he was overtaken for the lead by championship leader Tom Ingram. A last corner overtake saw Matt Nicoll-Jones take second place with Watson gaining holding on to third place.
Watson finished the season in seventh place overall in the standings with 372 points.
Success came early, with pole position, fastest lap and a win in the opening round at Brands Hatch, followed by second and third-place finishes in the next two rounds. A further win at Thruxton in round 9 of the series, saw Watson leading the championship with 230 points.
Watson eventually finished the season in fourth place on 640 points.
Watson scored his best result of the season when he and fellow McLaren GT “Young Driver” Ross Wylie finished seventh in the Silverstone 500 in May 2015, only 20 seconds behind the podium places. The race at Silverstone was preceded by races at Rockingham and Oulton Park. At Oulton Park in April 2015, Watson and his teammate Ross Wiley placed a ninth-place finish in the second race, whilst at Rockingham in May 2015, the team retired from the race on the opening lap following a collision.
Watson also raced in 4 races of the International Open GT Championship, scoring 1 race win and 1 pole position. In addition, Watson competed in the Sepang 12 hours and secured a class victory.
2016 – Blancpain GT Championship
For 2016, Watson raced in the Blancpain GT Series Endurance Cup with Garage 59 in a McLaren 650S GT3 as a member of the McLaren GT Young Driver Academy.
2016 also saw Watson make his debut at the famous Bathurst 12 hour race, where he finished a credible 9th overall on his first visit to the track.
Watson remained in the McLaren 650S GT3 racing with Garage 59 in the Blancpain GT Series Endurance Cup. Andrew's 2018 highlights included achieving pole position in the AM class at the Blancpain 24 Hours of Spa and pole position in the PRO Class at Paul Ricard. Watson also achieved an excellent podium position at the 1,000 kilometres of Paul Ricard as Andrew in the #58 Garage 59 McLaren qualified on the front row and led for the majority of the race, before eventually coming home in 3rd place - marking a proud moment in Andrew's career as he achieved his first overall podium finish in the Blancpain GT Series.
Watson also raced in the Blancpain GT World Challenge Europe for 3Y in a BMW M6 GT3, which included race victory in the Silver Class at Brands Hatch.
2019 – Blancpain GT Championship
Watson's 2019 season saw him compete in the European Blancpain GT Endurance Series with Andrew rejoining the Garage 59 team, following their switch to the Aston Martin Vantage GT3's for the 2019 Blancpain campaign.
Andrew also made his debut in the Aston Martin Vantage GTE as he featured in the FIA World Endurance Championship Rookie Test with Aston Martin Racing.
Watson, along with Garage 59 team-mates Oliver Hart and Roman De Angelis, finished third in the Silver class and 14th overall at Mount Panorama behind the wheel on an Aston Martin Vantage GT3.
(key) Races in bold indicate pole position (1 point awarded – 2002–2003 all races, 2004–present just in first race) Races in italics indicate fastest lap (1 point awarded all races) * signifies that driver lead race for at least one lap (1 point awarded – 2002 just in feature races, 2003–present all races)