The 32-year-old's contract with the Eskimos is a two-year deal worth $1.1 million, sources told TSN's Matthew Scianitti.
Harris will replace Mike Reilly, who officially signed with the BC Lions earlier Tuesday after six seasons in Edmonton.
"I'm excited to join the City of Champions and Edmonton Eskimos led by Brock Sunderland and Jason Maas," Harris said in a statement. "I'm very blessed to have their belief and I'm excited to get to work and start our pursuit to the Grey Cup with my teammates."
Harris led the Ottawa Redblacks to the 2018 Grey Cup game, which they lost to the Calgary Stampeders. He threw for 5,116 yards and 22 touchdowns in 17 games last season.