Heat president of basketball operations Pat Riley confirmed the team's intention to sign the forwards on Monday.
ESPN reported the 6-foot-10 McRoberts has agreed to a four-year deal worth an estimated $23 million, while Granger is set to receive a two-year, $4.8 million contract.
The two can't officially sign with the Heat until Thursday.
McRoberts, 27, averaged 8.5 points, 4.8 rebounds and a personal-best 4.3 assists in 78 games for Charlotte last season.
Selected by Portland in the second round of the 2007 NBA Draft, the Duke product has averaged 5.7 points and 4.2 rebounds in 350 career games with the Trail Blazers, Indiana Pacers, Los Angeles Lakers, Orlando Magic and Charlotte Bobcats.
Granger, a former All-Star, spent his entire career with the Indiana Pacers before being traded to Philadelphia at last season's deadline. After having his contract bought out by the Sixers, he finished the season with the Los Angeles Clippers.
The 31-year-old Granger's production has dropped the last couple seasons as he has battled injuries. For his career, he has averaged 17.4 points and 5.1 rebounds in 556 games.