Durbin receives a guaranteed base salary of $800,000 and can make an additional $1 million in reachable incentives, the source said. The deal is pending completion of a physical exam.
Durbin, who had generated interest from some clubs as a starter, is expected to pitch out of the bullpen for the Indians.
Durbin, 33, was a valuable bullpen contributor for National League East title teams in Philadelphia from 2008 through 2010. He averaged 64 appearances and 75 1/3 innings a season for manager Charlie Manuel during that span.
The Phillies explored the possibility of bringing back Durbin early in the offseason, but negotiations stalled after the team spent $120 million on free agent Cliff Lee and the Philadelphia front office decided to go with younger, more affordable alternatives in middle relief.
Durbin broke into professional ball with Kansas City in 1996 and pitched as a starter early in his career. He has an overall record of 36-44 with a 5.05 ERA in 11 seasons with the Royals, Indians, Diamondbacks, Tigers and Phillies.
Durbin previously pitched for Cleveland during the 2003 and 2004 seasons.
Texas, Tampa Bay, Boston and Kansas City were among the other clubs that expressed interest in Durbin this winter.
Jerry Crasnick is a senior baseball writer for ESPN.com