Bosh agreed to a five-year, $118 million contract, sources confirmed to ESPN.
The Houston Rockets also were in the hunt for Bosh, but the free agent has told them he is returning to Miami, sources said.
Bosh tweeted out the news of his return Saturday afternoon.
- Chris Bosh (@chrisbosh) July 12, 2014
In addition, sources say Miami is now pushing to keep free-agent guard Dwyane Wade.
Bosh opted out of the final two years of his deal -- worth $42 million -- with the Heat last month. He had planned to see what former Miami teammate James decided before making his free-agent choice. Earlier Friday, James told SI.com that he would be leaving the Heat to return to the Cleveland Cavaliers.
The Rockets thought they were nearing a deal for Bosh, with a source close to the situation telling ESPN.com's Marc Stein earlier Friday that the team believed it would have a commitment "soon."
Houston had offered him a maximum four-year, $88 million deal, sources said. It cleared out cap space by trading guard Jeremy Lin and a future first-round pick to the Los Angeles Lakers earlier Friday, a source said.
But Bosh chose the Heat instead, rejoining the team he's spent the last four years with alongside Wade and James.
Keeping Bosh was a huge part of Miami's immediate reaction plan after learning that James was leaving. He's an All-Star who averaged 16.2 points on 52 percent shooting last season, and now figures to potentially get many more shots in the Heat offensive scheme.
For his career, Bosh has averaged 19.2 points in 11 NBA seasons.
Bosh currently is in Ghana, and is expected to be there until next week, so it's unclear when he will actually sign the contract.
Wade, meanwhile, opted out of a deal that would have paid him about $42 million over the next two seasons.
But he seems inclined to staying in Miami.
"I know where I'm going," Wade told The AP on Thursday.
Pat Riley, in a statement addressing James' departure Friday, said the Heat mantra that he, managing general partner Micky Arison and coach Erik Spoelstra have cultivated will not be changing.
"Over the last 19 years, since Micky and I teamed together, the Miami Heat has always been a championship organization," Riley said. "We've won multiple championships and competed for many others. Micky, Erik and I remain committed to doing whatever it takes to win and compete for championships for many years to come. We've proven that we can do it and we'll do it again."
Information from ESPN.com's Jeff Goodman and The Associated Press was used in this report.