"I'm doing it because I hope we can negotiate an end to this for the good of the country and because I have high regard for the president and for Bob Mueller", Giuliani told the Post.
Giuliani served as mayor of New York City from 1994 through 2001.
The additions to Trump's legal team come after the March resignation of John Dowd, who had been the president's main lawyer on issues relating to the Russian Federation probe.
Since he left the mayor's office, Giuliani has been in private practice, most recently at worldwide law firm Greenberg Traurig. The notion that he will be able to quickly get a read on Mueller's team, said one source, is "not serious thinking".
Trump is known to be a hard client who does not listen to his attorneys' advice, according to lawyers who are familiar with his conduct.
Giuliani, who served as the mayor of NY between 1994 and 2001 and was in the post during the 9/11 attacks, was also the chief federal prosecutor in Manhattan for a long period in the 1980s.
At the outset of Giuliani's work for the President, he is expected to play a lead role in the interactions with the Mueller team.
Longtime friends, Giuliani often stood in for Trump during the 2016 presidential campaign, and perhaps his endorsement helped win Trump some votes among some groups of voters.
Now Giuliani, the Raskins and Sekulow will serve as the President's outside counsel, while Ty Cobb will continue to serve as the White House special counsel.
Giuliani, a Republican and ardent supporter of the president, reportedly traveled to Trump's Mar-a-Lago estate in West Palm Beach, Fla. last week to finalize the deal, the AP reported.
Giuliani declined to say whether Trump has made a final decision on whether to sit for an interview with federal investigators. Experts claimed Trump seemed like a tough client who does not pay heed to his lawyers' advice and some may fear potential conflict of interests, thus avoiding the job altogether.
Trump's legal team has been missing a big-name expert on criminal law since Dowd's departure.
-He played a vital role as NY mayor (1994-2001) during the September 11 attacks at the World Trade Center towers in 2001.