Dr Carson will assume the position of secretary for the Department of Housing and Urban Development (HUD), the president-elect’s transition team confirmed.
The 65-year-old former neurosurgeon has never held elected office and has no previous experience in the field of urban development.
Mr Trump and Mr Carson became locked in a war of words during the Republican presidential primaries, after the President-elect accused his rival of lying and mocked Mr Carson’s biography at a rally in Iowa.
In November last year, Mr Trump accused Mr Carson of having “a pathological disease” and compared the surgeon to a child molester, saying there was “no cure” for his alleged condition.
"I'm not saying anything other than pathological is a very serious disease. And he said he's pathological, somebody said he has pathological disease," Mr Trump told CNN.
"You don't cure these people. You don't cure a child molester. There's no cure for it. Pathological, there's no cure for that."
As with everyone appointed to Mr Trump’s cabinet so far, Dr Carson has vocally opposed LGBT rights in the past and once compared gay marriage to bestiality.
During a radio interview in April, Dr Carson said Mr Trump “has some major defects, there’s no question about it” when asked about the billionaire’s leadership credentials.
Dr Carson later came out in support of the President-elect, saying Mr Trump could “restore the confidence of the American people”.
Last month, Dr Carson reportedly considered turning down a cabinet role, saying he "had no government experience".
“Ben Carson has a brilliant mind and is passionate about strengthening communities and families within those communities,” Mr Trump said in a statement following the appointment.
“Ben shares my optimism about the future of our country and is part of ensuring that this is a presidency representing all Americans. He is a tough competitor and never gives up.”
Dr Carson said he was “honoured” by the opportunity, days after hinting at his imminent appointment to the Trump cabinet in a Facebook post.
“I feel that I can make a significant contribution particularly by strengthening communities that are most in need,” he said.
“We have much work to do in enhancing every aspect of our nation and ensuring that our nation’s housing needs are met.
“I grew up in the inner city and have spent a lot of time there, and have dealt with a lot of patients from that area and recognise that we cannot have a strong nation if we have weak inner cities.”
Mr Trump’s cabinet appointments have so far generated controversy, with several of the nominees accused of being white supremacists.
The most widely criticised has been the appointment of right-wing Breitbart News founder Steve Bannon as chief strategist.
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