The All-Star outfielder batted .274 with nine home runs, 57 RBIs, and 42 steals with the Atlanta Braves in 2012. Bourn joins outfielder Nick Swisher, who also signed a four-year deal with Cleveland.
Bourn’s deal is still pending, due to a physical.
By adding Bourn, Cleveland will be required to forfeit their third pick in the First-Year Player Draft in June as a penalty.
The New York Mets were also reportedly interested in Bourn, and offered the same amount as Cleveland, but were unwilling to concede the 11th overall pick in the draft. Bourn received a one-year qualifying offer from the Braves for $13.3 million, but decided to test the free-agent market.
Bourn, 30, entered the Majors with the Philadelphia Phillies in 2006, and spent nearly four seasons with the Houston Astros before being dealt to the Braves in 2011. He has a .272 career batting average with 22 home runs in seven seasons. Bourn is also a two-time Gold Glove winner, and a three-time steals leader with a total of 276 in his career.
The Indians are expected to be a threat on the base paths in 2013 with Bourn, Jason Kipnis and Drew Stubbs.
The additions of Bourn and Swisher represent a major facelift for the Indians, who have struggled in American League Central. The Indians have failed to finish with a record above .500 since 2007 when they won the division, but lost to the Red Sox in seven games in the American League Championship Series.
Cleveland finished with a 69-94 record in 2012, and fired manager Manny Acta before the end of the season. Former Boston Red Sox manager Terry Francona was hired in October.