ESPN’s Adam Schefter was the first to report the deal, which was confirmed by Bush on his Twitter account. No details of the agreement were provided.
The 30-year-old Bush reportedly visited New England this week, but came away without a deal. Now the nine-year veteran will return to California, where he had a record-setting college career at USC.
Bush spent the past two seasons with Detroit, but was slowed by an ankle injury in 2014. He ran for only 297 yards and had 40 catches for 253 yards last season, following a very productive 2013 season that included 1,006 yards rushing along with 54 catches for 506 yards.
Before his two years in Detroit, Bush spent two seasons in Miami and five seasons with the New Orleans Saints, who drafted him second overall in 2006. Overall in his career, Bush has combined for 5,465 yards and 35 scores on the ground and 466 catches for 3,489 yards and 18 touchdowns receiving.
Bush fills a void for the 49ers at running back after Frank Gore left the franchise after 10 seasons to sign with the Indianapolis Colts.
The 49ers also return Carlos Hyde and Kendall Hunter at running back. Hyde rushed for 333 yards and four touchdowns as a rookie in 2014 while Hunter missed the season with a knee injury.