Bush's contract is worth $16 million over four years, including $4 million guaranteed, a league source told ESPN NFL Insider Adam Schefter.
The Lions also agreed to deals with former Houston Texans safety Glover Quin, cornerback Chris Houston and former Seattle Seahawks defensive lineman Jason Jones on Wednesday. The Lions announced Quin inked a five-year deal.
The 29-year-old Bush proved that he can be an every-down tailback in Miami, rushing for 2,072 yards and 12 touchdowns in two seasons with the Dolphins.
He called the Lions' offense "a running back's dream."
"The first thing we talked about, we're watching film, seeing those safeties deep ... it's a running back's dream. We have to be able to run the ball in that situation. That's part of the reason I wanted to come here and be part of a balanced attack and take the pressure off Calvin Johnson and Matthew Stafford."
Lions great Barry Sanders welcomed him to the Lions on Wednesday afternoon, in a tweet.
"Proud to be a @DetroitLionsNFL and excited to welcome @ReggieBush to the family," he wrote.
In 2012, Bush played in every game for the first time since 2006 and fell just shy of his second consecutive 1,000-yard rushing season, finishing with 986.
In 91 career games, Bush has 4,162 yards rushing, 2,730 receiving and 48 touchdowns (29 rushing, 15 receiving, four return).
Quin led the Texans with 84 tackles last season, along with two interceptions, two forced fumbles and a sack.
Quin moved from cornerback to safety when Wade Phillips took over the Texans' defense in 2011. The 27-year-old defensive back has 314 tackles and five sacks in 63 career games.
"There are a couple things that we look for in a safety, you know, and Glover hits all of those," Lions coach Jim Schwartz said. "Multi-dimensional ability, he's a guy that played corner in college. I remember looking at him when he came out of New Mexico and as physical as he played, the first thing that came to mind is this is a guy that can make the move to safety."
Houston agreed to a five-year deal to return to the Lions. The terms of Jones' agreement weren't immediately known.
"I'm excited that it's all over," Houston told the Detroit Free-Press. "I've been through free agency before, and it was crazy that time. It was crazy this time, also, but I'm just happy that I have a home, a place to go and finish out my career. I'm not one of those guys out there who's worried about where they're going to be, so I feel pretty good."
Houston had two interceptions, two forced fumbles and 56 tackles last season for Detroit, his third season with the Lions. He had a career-best five interceptions in 2011.
In 87 career games, he has 332 tackles, 11 interceptions and four forced fumbles.
Jones' agent tweeted the news of his client's agreement with the Lions.
Jones went to high school in Lathrup Village, Mich., and played college football at Eastern Michigan. He was a backup defensive tackle last season for the Seahawks. His season ended in December due to a lingering knee injury.
But the 6-foot-5, 276-pound Jones could play a bigger role with the Lions, who may lose defensive end Cliff Avril to free agency.
Detroit also released veteran Kyle Vanden Bosch last month.
Information from ESPN.com NFC North blogger Kevin Seifert, ESPN.com AFC East blogger James Walker and The Associated Press was used in this report.