Miller's agents already have begun reaching out to other teams who may have interest in Miller, according to sources.
The move will save the Heat nearly $17 million in luxury taxes this season and reduce their expected tax bill, projected to be $33 million, by half. The Heat still owe Miller $12.8 million over the next two seasons as part of a contract he signed in 2010.
"I understand the business side of basketball," Miller told The Associated Press. "It's a combination of being very, very thankful for the opportunity that I've had, but it hurts that we had a chance to do something very, very special and I'd love to have been a part of it."
Chris Bosh, in Mumbai, India, on Wednesday to promote the NBA, called Miller's release "extremely tough."
"I don't think we can replace it. Hopefully we can make up ground because what he brought to the team is going to be difficult to replace," Bosh said. "I just hate that he's going to be picked up by another team, to defend against him now, we had a great time with him and he was a huge part of the team and of our locker room and it's going to be difficult moving forward without him."
The decision reveals a bit of a split in the Heat front office. Team president Pat Riley said several times since the end of the Finals that he didn't want to use the amnesty on Miller and he wanted to bring the back-to-back champions back intact for another run next season.
"After many discussions internally and a sincere effort to explore the trade market, we made a very difficult decision to use our Amnesty provision on Mike Miller," Riley said. "Mike had an incredible impact on the Miami Heat; helping us to three finals appearances and winning back-to-back World Championships. This was a very difficult decision for me personally, the Arison family, Erik and the entire Miami Heat organization. Mike was one of the best we have ever had here, and will be sorely missed. We wish Mike, his wife Jennifer and their family nothing but the best."
Riley went so far as to say "we're not using the amnesty" in a conference call with reporters last week.
"I want to try to keep this team intact as long as we can because we have a championship basketball team here," Riley said. "I would hate to break any part of it up, that is productive and leads to winning."
Riley said the choice on Miller, though, ultimately would be an ownership decision. It appears principal owner Micky Arison and his son, team CEO and part owner Nick Arison, decided to overrule Riley with the huge tax bill the facing the Heat. For the 2012-13 season, the Heat paid $13.3 million in luxury tax, the most Arison ever has paid and more than twice what he paid when the Heat won the title in 2012.
It is possible the Heat released Miller to set up another deal. They still have their $3.2 million mid-level exception and are one of the teams interested in free agent center Greg Oden.
Miller, who has been a playoff hero for the Heat during their past two championship runs, has battled numerous injuries. He had four surgeries after signing with the Heat to his thumbs, shoulder and to repair a sports hernia. Miller also has had back problems. He averaged 46 games played over the past three regular seasons.
But 2012-13 was his healthiest year. He played in 59 games but averaged career lows in points (4.8) and minutes (15.3). He played in all seven games in the Finals, starting the last four games, averaging 5.3 points and shooting a remarkable 61 percent on 3-pointers.
Information from The Associated Press was used in this report.