Cobb, 68, a seasoned white-collar defense lawyer who joined the White House team last August from his firm at Hogan Lovells, had repeatedly urged Trump to agree to the interview in order to disperse the cloud of questions hanging over his presidency.
"Emmet Flood will be joining the White House staff to represent the president and the administration against the Russian Federation witch hunt", White House press secretary Sarah Huckabee Sanders said in a statement.
Referring to Mr. Ty Cobb as "a friend of the president" who has done a "terrific job", Ms. Sanders said the attorney will be retiring at the end of the month.
"Some time after the campaign is over, they set up a reimbursement, $35,000 a month, out of his personal family account", Giuliani, a new addition to Trump's legal team, told The New York Times In total, Trump reimbursed Cohen $460,000 or $470,000 for the Daniels payment, which Cohen made "on his own authority", and other "incidental expenses", Giuliani said, adding that he was "not clear that" Trump knew about the Daniels payment at the the time.
He's known for his aggressive advocacy and may take a more adversarial approach to Mueller.
'Governance left the room a very long time ago'
Nearly 300 women may have died in the United Kingdom because they missed out on breast cancer screenings due to a computer error. Despite his shock, Mr Gough said he admired the Health Secretary for "getting up and not trying to hide the truth".
Trump on Twitter Wednesday promoted a comment from attorney Joseph diGenova describing the questions as an "intrusion" into the president's constitutional powers and saying it would be "outrageous" to ask the president what he was thinking when firing members of the executive branch.
Separately, Giuliani told Bloomberg News that the legal team "would be inclined" to allow the interview, but said if Mueller already believed former Federal Bureau of Investigation director James Comey's version of events, then it would be leading Trump "into the lion's den".
Mr Trump's previous lead lawyer on the case, John Dowd, quit in March, reportedly because he felt his client was ignoring his legal counsel.
In early March, Trump met in the Oval Office with Flood to discuss the possibility of joining the president's legal team.
A subpoena to force the president before a grand jury could start an explosive legal battle that eventually reaches the US Supreme Court.
What is Mueller's latest move?
In a Tuesday tweet, Trump blasts what he calls a "rigged system".