The transition team described Carson as "a distinguished national leader who overcame his troubled youth in the inner city of Detroit to become a renowned neurosurgeon."
Carson said he was honoured to accept the post. "I feel that I can make a significant contribution particularly by strengthening communities that are most in need," he said in the statement.
Carson, 65, is the first African-American picked for a Cabinet spot by Trump, who takes office on January 20 and has been gradually filling out his administration since beating Democrat Hillary Clinton in the November 8 presidential election.
Carson, a highly respected neurosurgeon at Johns Hopkins Hospital in Baltimore, had been considered for US surgeon general and head of Health and Human Services Department.
Like many of the initial field of 17 Republican presidential hopefuls who vied for the party's 2016 White House nomination, Carson was a frequent Trump target during the campaign.
But he became one of his most high-profile African-American supporters after Trump secured the nomination.
At HUD, Carson would lead an agency whose mission has been to help middle- and low-income people find homes.
It also runs a programme aimed at replacing distressed public housing with mixed-income neighbourhoods.
The department also oversees mortgage lending and other housing programmes.
In a July 2015 opinion piece for the Washington Times, Carson gave some indication of his views on housing policy, criticising actions by the Obama Administration to reduce racial segregation as having the potential to "make matters worse."
- AAP
