Trump's decision, announced early Monday by his transition office, comes as the real estate mogul continues a series of interviews, meetings with aides and other deliberations aimed at forming his administration.
In a statement, Trump says he's "thrilled to nominate" Carson, saying he "has a brilliant mind and is passionate about strengthening communities and families within those communities."
Carson has been coy about joining the new administration, saying shortly after Trump's election victory that he wasn't certain he'd fit into a Cabinet-style role. The discussion at that time centered on speculation that Carson might be selected to head the sprawling Department of Health and Human Services.
According to the Associated Press, Trump's statement Monday says, "Ben shares my optimism about the future of our country and is part of ensuring that this is a presidency representing all Americans."
Carson was among the 16 Republican candidates who challenged Trump for the Republican nomination. He was a favorite of religious conservatives and a strong fundraiser, but his team burned through money quickly and he failed to win any of the early primary contests.
Trump treated Carson harshly during the primary, saying he had a "pathological temper." Still, Carson quickly endorsed Trump after he dropped out of the contest.
As a Trump supporter, Carson was both loyal and critical. He conceded that Trump had "major defects" and said at one point that he would have preferred a scenario other than Trump winning the Republican primary.