Atchison's deal, which was finalized Tuesday, includes a team option for 2016. Financial terms were not immediately available.
The 38-year-old Atchison has been major contributor out of Cleveland's bullpen this season, posting a 6-0 record and a 2.95 ERA in 53 appearances. He signed a free agent minor league contract with the Indians in January and made the 25-man roster out of spring training.
Cleveland manager Terry Francona, who had Atchison on his last two teams in Boston, was "thrilled" by the news.
"He's great in the bullpen. Guys look up to him. He's just a really good influence, and he gets people out," Francona said in Minnesota, before the Indians started a three-game series against the Twins. "And because of guys like him and their attitude, it's allowed our bullpen to kind of flourish."
Atchison has held hitters to a .218 average and ranks among American League relief leaders in wins, inherited runners scored and innings.
"I think Atch really values a place where he's comfortable, where he knows he's respected by his teammates, by the coaches, by the press, everybody," Francona said. "And I think it's a good fit for him and us."
Atchison is 16-10 with a 3.51 ERA in 258 major league games since breaking in with Seattle in 2004, six years after being drafted in the 49th round out of TCU. He pitched two seasons for the Mariners, one for the San Francisco Giants and two for the Hanshin Tigers in Japan. Then he signed with the Red Sox in his return to the majors and spent three years with them. Atchison pitched in 50 games last season for the New York Mets.
Despite the age jokes, the Indians have valued his presence.
"What'd they give him, a year, an option and an AARP card?" Francona quipped.
Raburn, who has been bothered by soreness in his right wrist most of the season after hurting it in spring training, aggravated the injury last week with a diving catch. He's batting .191 with three home runs and 21 RBIs in 188 at-bats over 70 games.