His appointment renews his professional partnership with Steve Blamer, who previously ran the London agency before becoming the chief executive of Grey Worldwide North America.
As the chief creative officer and president of Grey in North America, Mellors will be responsible for boosting the output of some 500 creatives across seven Grey offices in the US and Canada.
Mellors seemingly quit the business for good last summer after more than 30 years, when he handed over creative control to Dave Alberts.
Since then he has been working to complete his qualification as a psychotherapist while taking an arts appreciation course. Meanwhile, he has recorded a new series of Double Cross, the gameshow he hosts, for BBC4.
"I left the business because I felt I needed a change and a rest," Mellors said. "But I missed the thrill of the business, which I couldn't get anywhere else."
Mellors, 57, who will move with his wife and two daughters to New York before beginning work in September, said he expected to remain in the job for between three and five years while a long-term successor was put in place.
Blamer originally asked his one-time associate to help to identify candidates for the role before suggesting that Mellors should take the position himself.
Blamer said: "Over the past several months, as I talked to candidates, I kept asking myself: 'Does this person fulfil our criteria as well as Tim?' -and the answer was always 'no'."
Mellors is almost as famous for his battle to overcome drink and drugs as for his agency career, which included the creative directorships of Gold Greenlees Trott and Publicis. He is best known for his British Airways work at Saatchi & Saatchi and for creating Abbey National's "Abbey endings" campaign.