He was instrumental in successfully lobbying for that ban to be dropped and is known to have always been pressing his old friend Trump to scrap the Obama-led nuclear pact.
Jay Sekulow, a lawyer on Trump's legal team, did not immediately respond to CNBC's request for comment on Giuliani's announcement.
Giuliani's engagement with Trump's domestic legal woes have been every bit as incendiary.
Rudy Giuliani, the former NY mayor and the latest appointee to President Donald Trump's legal team, attends the 2018 Iran Freedom Convention for Human Rights & Democracy, in Washington, D.C., on May 5.
Wellcome pledges £2m after new Ebola outbreak confirmed
Over 21 suspected viral haemorrhagic fever and 17 deaths have been reported around Ilkoko Iponge in the past five weeks. Médecins Sans Frontières is setting up a treatment centre for the management of cases in Bikoro health zone.
It contradicted Trump's previous denials and was portrayed in many media outlets as a "blunder" by Giuliani.
Avenatti earlier this week challenged Giuliani to a head-to-head debate. Cohen's lawyer, Stephen Ryan, said the raids were the result of a referral from Mueller's team, and were reportedly signed off on by Deputy Attorney General Rod Rosenstein, who gained oversight over the special counsel's probe following Attorney General Jeff Sessions' recusal. But he added, Giuliani now recognizes that the new task is "all consuming" and "lasting longer than initially anticipated".
Originally, Giuliani and the firm believed he would not be working for Trump this long.
Giuliani made explosive headlines after revealing that Trump reimbursed Cohen for paying Daniels, in order to stave off allegations that the payment was a campaign contribution.
Indian refiners in no rush to seek alternatives to Iranian oil
After sanctions were eased as part of the nuclear agreement, Iran ramped up production to about 3.8 million barrels a day. And there is no guarantee that Iran's major customers will comply with new sanctions.
Significantly, Trump has taken to the Fox News airwaves to sing the praises of a quartet of "absolute warriors" - relatively junior GOP congressmen Jim Jordan, Mark Meadows, Matt Gaetz and Ron DeSantis.
Mueller is investigating claims of Russian interference in the 2016 presidential election and whether Trump's campaign colluded in that effort.
Cobb is known to have vainly fought to curb Trump's Twitter attacks on Mueller and the Justice Department and to privately blame the president for the rancid atmosphere between the White House and the special counsel. Perhaps Giuliani's former bosses would even have granted him a sabbatical, and then allowed him back, if the words coming out of his mouth since joining Team Trump hadn't become so thoroughly mortifying by association. More likely, as others have speculated, "America's Mayor" was told he had 24 hours to cough up a letter announcing his departure, or the firm would cough it up for him.
"That was money that was paid by his lawyer, the way I would do, out of his law firm funds", he said on Fox News.
EPL: Wenger speaks on what successor 'must do' at Arsenal
Wenger will leave the Gunners at the end of the season, having led the club to three Premier League titles and seven FA Cups. The Frenchman's final game in charge of the club will be against Huddersfield on Sunday.