Scaramucci, who had initially supported Republican candidates Scott Walker and then Jeb Bush, called Trump a "hack politician" during a Fox Business appearance in 2015.
Asked whether Trump was aware of his comment, he said the president reminds him of those words on a daily basis.
"He brings it up every time. I personally apologise," the 53-year-old smooth-talking Wall Street financier said and called it one of his "biggest mistakes."
Scaramucci, who currently serves as the senior vice president and chief strategy officer at the Export-Import Bank, will officially start his new role on August 15.
During his introductory appearance at the White House, Scaramucci appeared relaxed and expressed a desire to improve the Trump administration's relationship with the US media.
He praised Trump and said he was "proud" to join his administration. "The ship is going in the right direction. I think we've got...The direction very, very clearly," he told reporters at the White House after his appointment yesterday.
"The president has really good karma. And the world turns back to him...I think as members of Congress get to know him better and get comfortable with him, they're going to let him lead them to the right things for the American people.
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