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.
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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."
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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.
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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."