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.
"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.
Unless the Indians can work a trade, they will have to pay Fultz his entire $1.5 million contract for 2008.
On Sunday, the club acquired left-hander Craig Breslow on waivers from Boston, possibly to take Fultz's middle relief role.
"He gets the first shot," Shapiro said. "He's a guy that at this time a year ago we would never have had a chance to get him."
The 27-year-old Breslow has struck out 383 in 357 2/3 innings in six minor league seasons. In 27 career games with San Diego and the Red Sox, he is 0-2 with a 2.86 ERA.
"He gets out lefties and right-handers, but has been very successful against left-handed hitters," Shapiro said. "When he has struggled at times, it has been with his command, not throwing strikes."
Breslow reported to the Indians on Monday and said he wasn't too surprised to be claimed by Cleveland.
"It's been a whirlwind couple of days, but I'm excited to be here," he said. "My agent told me the Indians had been following me the last couple years. I watched them play the Red Sox during the playoffs on TV from my home in Connecticut. Now, I hope I can help them win."
Breslow is scheduled to make his first appearance for the Indians in relief Tuesday against the New York Yankees.