Anderson will receive a one-year deal worth approximately $1.7 million, with a player option on a second year, according to a source close to the player.
Anderson drew interest from three teams, but the source said that "Miami was always No. 1" after he emerged as the Heat's best big man after joining the team in January.
He averaged 4.9 points and 4.1 rebounds off the bench in 42 regular season games and 6.4 points and 3.8 rebounds while shooting a remarkable 81 percent from the field in the postseason.
The Heat had made bringing Andersen back an offseason priority but are limited somewhat financially because they are facing a $30 million luxury tax bill this upcoming season.
Yahoo! Sports had earlier reported the agreement.
According to the source close to Andersen, after he signs the deal he will head back to his offseason home in Texas to relax and hunt hogs.
Information from ESPN.com's Marc Stein, Brian Windhorst and Jared Zwerling was used in this report.