As an 18-year-old rookie, he scored 11 goals playing right wing (shifting from his natural centre ice position) with veterans Doug Shedden and Terry Ruskowski.

Simpson continued to blossom in Edmonton, shifting to the left wing and playing on a line with future Hall of Famers Mark Messier and Glenn Anderson.

On July 16, 1993, the San Jose Sharks presented Simpson with an offer sheet which he accepted, joining the club as a free agent.

However, the Oilers protested the deal that would see Simpson earn just $130,000 per season (the NHL minimum) while receiving a sizeable $1,790,000 "reporting bonus" for merely showing up at Sharks training camp.

[12] When rumours began to swirl that the Buffalo Sabres were also preparing an offer sheet for Simpson, the Oilers instead traded him there.

Arguably one of the most proficient snipers in NHL history, he holds the record for best career shooting percentage (minimum 800 shots) with 23.66%.

He also holds the record for best career playoff shooting percentage (minimum 80 shots) with 33.65%, well ahead of second place Jake Guentzel.

In 1998, Simpson joined CTV Sportsnet as a colour commentator for Edmonton Oilers regional games, as well as the network's weekly national broadcasts.

After the 2006–07 season, he resigned from his position with the club to take a job as a colour commentator for CBC Television, alongside former Sportsnet partner Jim Hughson.

[17][18] When Rogers Media gained the NHL rights in 2014, the pair shifted to and re-joining Sportsnet, until Hughson retired from hockey broadcasting.

On March 22, 2008, Hughson and Simpson called the NHL game between the Edmonton Oilers and the Colorado Avalanche at 1 p.m. MDT.

In 2009, Simpson participated in the first season of CBC's Battle of the Blades, a made-for-TV figure-skating competition that paired eight former NHL stars with female figure skaters.

On June 21, 2012, Simpson married Canadian figure skater Jamie Salé, whom he had "known for years from the Edmonton skating scene".