The Burkina Faso international, 21, has spent recent seasons on loan at Dutch clubs Vitesse Arnhem and Ajax and will now move to France on a contract until 2022.
Lyon wrote on Twitter: "It is official: Bertrand Traore is Lyonnais! A transfer for 10m euros (£8.8m) and a five-year contract."
Reports have suggested the fee includes a sell-on clause and other potential add-ons.
A press conference staged by Lyon to unveil Traore began in bizarre fashion, with a seat left empty at the table while club president Jean-Michel Aulas and coach Bruno Genesio discussed a range of other matters.
Aulas, quoted by L'Equipe, made mention of "technical difficulties" in concluding the transfer and added that Traore "will not be present for the return to training on Tuesday".
But the player was eventually introduced during the press conference and posed for photographs with the club's shirt.
He told OLTV: "I am very happy to be here, to be Lyonnais.
"Lyon has always been an impressive club, with big players and a great history. It is an honour for me to play here.
"When I came here with Ajax a few months ago, I was attracted by the philosophy of the club, with several young players from the academy, and the magnificent Parc OL.
"With Ajax, we had a bit of a similar style of play and that enticed me to come here.
"I am coming to bring something extra to OL and I hope to continue progressing and to learn with the coach and my new team-mates."
Traore officially joined Chelsea in 2013, having previously appeared for them as a trialist after emerging from Auxerre's academy.
He never established himself in the first team and, after his recent loan moves, is looking to carve out a long-term role for himself.
He said: "I have been looking to have stability and, in signing a contract with OL, I could not ask for more. I have the time to show everyone what I can do."
