Chelsea boss Jose Mourinho confirmed the move by saying: "It's a question of only a few details.
"He provoked a lot of tears when he left on Monday because he's a wonderful boy and was a very good player for us.
"But he had a good offer from Lyon and their offer to Chelsea is very good. He wants to go and we couldn't break the legs of a boy like this to stop him."
Mourinho brought Tiago to Stamford Bridge on a four-year contract in July 2004.
Tiago made regular appearances for Chelsea last season, playing in 34 of the 38 league games and scoring four times, but is down the pecking order after Essien's arrival