The team announced the deal on Wednesday:
ESPN's Adam Schefter first passed along word of the signing.
Jason La Canfora of CBS Sports reported the details of the contract on Friday:
Bush spoke about joining his fourth NFL team on Twitter:
Bush has flashed high-end playmaking ability since his days at USC. That wasn't lost on head coach Jim Tomsula, per NFL.com's Marc Sessler:
A lack of consistency running between the tackles and nagging injury woes have hampered him, though. It's unlikely that will change as he heads into his age-30 season.
He's coming off a campaign in which a few ailments, including an ankle issue that lingered, limited him to just 11 games. Even when active, his role was diminished as the Detroit Lions leaned on Joique Bell and Theo Riddick more heavily.
The question after the Lions decided to let Bush go was how much he had left in the tank.
Before his down 2014, he put together three straight seasons of at least 200 carries. He rushed for over 3,000 yards and scored 16 rushing touchdowns over that span with the Lions and the Miami Dolphins. He's also a proven asset in the passing game, with more than 460 career catches.
For his part, Bush sounded upbeat about his health after the season, per Dave Dye of Fox Sports Detroit:
I think I have a lot left to give this game. My body still feels pretty good. I don't feel worn down. I don't feel beat up. As a running back, nine years in this league can make you feel that way. But I still feel pretty good. I'm planning on playing for a while.
Now, Bush will get a chance to back up those comments with his new team.
Bleacher Report's Michael Schottey likes the signing, particularly when paired with young bruising back Carlos Hyde, claiming him to be a perfect complement to Hyde's old-school, downhill running style.
The biggest thing for the 2006 No. 2 overall pick is staying healthy. He's a smaller back with a lot of mileage on his body. Making it through an entire season without an injury sidelining him would be a terrific first step toward success.
Beyond that, he's still illustrated the necessary explosiveness to make big plays. A limited role with around 10 carries a game to go along with plenty of work on passing downs figures to maximize his value without putting him at too much risk.
His season-long outlook should become clearer once training camp gets underway. Expectations should be kept within reason, but it's a signing that certainly has some upside for San Francisco.