The Associated Press reported Monday afternoon the contract would be pending a physical and wasn't finalized.
After pitching a total of 1 2/3 innings in the big leagues in a two-year span, Kazmir returned to post a 10-9 record with a 4.04 ERA in 29 starts with the Indians in 2013.
Kazmir joins Jarrod Parker, A.J. Griffin, Dan Straily and Sonny Gray in Oakland's projected rotation and could give the A's sufficient depth to entertain trade offers for the frequently injured Brett Anderson.
According to The San Francisco Chronicle, the Kazmir signing also brings an end to the A's attempt to re-sign right-hander Bartolo Colon.
Kazmir, a first-round draft pick by the New York Mets in 2002, made the American League All-Star team with Tampa Bay in 2006 and 2008.
His career quickly unraveled due to a combination of injuries and mechanical issues, and the Angels released him in June 2011.
But Kazmir worked his way back in a stint with the Sugar Land Skeeters in the independent Atlantic League, attracting the attention of Edwin Rodriguez, a minor league manager in the Cleveland system, last winter in Puerto Rico.
After winning a spot in the Cleveland rotation in spring training, Kazmir struck out 162 batters in 158 innings. He was particularly effective at home, going 7-2 with a 3.86 ERA in 14 starts at Progressive Field.