The trio had been expected to opt out of their existing agreements to free up salary space for the Heat, then take less money in the short-term on fresh contracts with Miami.
The Heat were beaten by San Antonio in the NBA Finals and the decision will allow the team to add new players.
"Today we were notified of Chris's intentions to opt-out of his contract," Heat President Pat Riley said in a statement.
"Chris is one of the most versatile and dynamic big men in this league, and he has been an instrumental key to our championship success over the last four seasons.
"We look forward to meeting with Chris and his agent in the coming days to discuss keeping him in Miami for many years to come."
The 30-year-old Bosh averaged 16.2 points and 6.6 rebounds and made his ninth consecutive All Star appearance last season.
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