The Indians then created a bullpen opening, parting ways with left-hander Aaron Fultz.
Lee, demoted to the minors for a brief time last season, pitched five scoreless innings against the New York Mets on Saturday.
That outing won the competition with fellow left-handers Jeremy Sowers and Aaron Laffey, who were sent to the minors.
"Cliff reported in outstanding shape and as camp went along, pitched better and better," general manager Mark Shapiro said. "The other two improved, too. They are definitely guys who can impact our rotation this year."
Lee is scheduled to pitch Cleveland's final spring game in Florida on Thursday, then start an exhibition game at Class A Kinston (N.C.) on April 1. The Indians will not need a fifth starter until the second week of the season.
"I'm happy, of course," Lee said. "This sure beats a year ago."
The 29-year-old lefty endured a rough 2007 season. Expected to be Cleveland's No. 3 starter after getting 46 wins over the previous three seasons, Lee strained an abdominal muscle early in camp, opened the year on the disabled list and never got comfortable. He struggled to a 5-8 record and 6.29 ERA, even trying to work out his problems by working in relief for the first time.
"I had a bad year and want to make up for it," Lee said. "I'm healthy now and my goal is exactly what it always is: make every start; work as long as I can in each of them; and give my team a chance to win.
"I can't control, wins, losses, stuff like that. But this is a heck of a good team and I'm excited and happy to be part of trying to get back to the postseason."
Fultz won't get that opportunity in Cleveland. In 8 1/3 innings over seven spring outings, the 34-year-old veteran had an 11.88 ERA.
"The decision wasn't made solely on spring training," Shapiro said. "Aaron pitched very effectively for us last year before getting hurt and hasn't returned to his previous level."
Fultz started 3-1 with a 1.71 ERA in his first season with Cleveland in 2007, then missed a month with a strained muscle in his right side. He was only 1-2 with a 4.60 ERA in his return.