The Falcons announced the agreement on Thursday, but did not release the terms.
The 30-year-old Jackson had 1,042 yards rushing and four touchdowns with the Rams last season. It was his eighth straight season with more than 1,000 yards rushing.
Jackson has 10,135 yards rushing, the most of any active player. He set career highs with 1,528 yards rushing and 13 touchdowns with St. Louis in 2006.
Turner's average of only 3.6 yards per carry last season set a career low. The Falcons released Turner, defensive end John Abraham and cornerback Dunta Robinson on March 1.
Jackson averaged 4.1 yards per carry with the Rams.