"It's a running back's dream," Bush said. "One of the reasons I wanted to come here is to be able to bring a balanced attack."
Bush adds to a strong offense led by record-setting All-Pro receiver Calvin Johnson. The second overall pick in 2006 by New Orleans, Bush rushed for 986 yards for Miami last season after gaining 1,086 yards in 2011, his first year with the Dolphins.
"The thing that was important to us was not just the talent of Reggie Bush, but also the way those talents complemented the other players we have on offense," coach Jim Schwartz said. "That was really the basis of our interest in Reggie."
The Lions also landed safety Glover Quin and defensive end Jason Jones and retained cornerback Chris Houston.
All-Pro safety Goldson gets a five-year contract worth $41.25 million. He receives $8.25 million per year and $22 million in guaranteed money. He spent the past two seasons on one-year contracts with the 49ers, including last year with the franchise tag for $6.2 million.
"Hard work really pays off. I remember signing up to play football, hiding it from my mom," as a youngster growing up in Harbor City, Calif., Goldson said. "My journey, I wouldn't say it was rough, but it was a little rocky."
Free agent defensive back Charles Woodson had a meeting with the NFC champion Niners in the Bay Area on Wednesday, according to his agent, Carl Poston.
Also Wednesday, former Kansas City Chiefs defensive end Glenn Dorsey signed a two-year contract after meeting with the Niners. The deal could pay Dorsey up to $7 million with incentives, a person with knowledge of the contract told The Associated Press. The person spoke on condition of anonymity because terms weren't announced.