Bibby is expected to play for his new team Thursday night when it hosts the Magic. On Monday, Bibby agreed to forfeit the $6.2 million he was owed by the Washington Wizards for next season so that he could become a free agent and sign a league minimum contract with the Heat.
The move shocked many in the league, including players and former teammates.
"It is really not [anyone's] decision to make," said Bibby, who has signed contracts worth more than $100 million during his 13-year career.
"I make the money, I decide what I do with it, it doesn't matter what anyone thinks of it," Bibby said. "My financial stuff is my business. It is always tough to give up money. I've won and lost in my career and I'm at a stage where I want to be happy."
Happiness, Bibby believes, is joining a Heat team loaded with stars like LeBron James, Dwyane Wade and Chris Bosh that has championship hopes but hasn't gotten steady point guard play this season. Bibby, who said he's watched the Heat often, believes he can represent that missing element.
"They're on TV a lot and you're just in awe of the way they play," Bibby said. "It looks like everybody wants to win and everybody has the right attitude. I thought it would be a good fit for me here.
"I'm a pretty smart player, I'll just get the ball to the guys where they need the ball at ... I'm not the type of player that needs shots to be effective."
Heat coach Erik Spoelstra said he was not focused on where Bibby's minutes would come from or whether he would replace current starter Mario Chalmers, which is what most expect will eventually happen. Spoelstra said he and the rest of the team were just pleased they could acquire someone with Bibby's resume at this point in the season.
"We're very excited about an opportunity like this, especially late in the year," Spoelstra said. "We weren't necessarily expecting this about a month ago. We think he can really help."
The opportunity arose when the Atlanta Hawks traded Bibby to the Wizards for Kirk Hinrich last week, a trade that dismayed and surprised Bibby. He was never told about the deal that would make him a backup to Wizards rookie John Wall until shortly before a Hawks game in Phoenix last Wednesday, when the deal was nearly finalized.
"I just felt that out of respect they could have told me that morning," Bibby said. "I saw everybody that morning and I wasn't told until it happened. It is not a big deal, it happens in this league and it is time to move on."
When he heard Bibby was upset, Hawks coach Larry Drew told reporters Wednesday in Atlanta: "It's been my experience in all the years I've been involved with the NBA, that is the way you handle it."
Brian Windhorst covers the NBA for ESPN.com.