The former Tottenham boss has signed a two-year contract with an option for a third.
Mauricio Pochettino has been appointed Chelsea manager on a two-year deal.
The former Tottenham coach, who has been out of work since leaving Paris St Germain last year, will take over from interim boss Frank Lampard who oversaw his final game in charge against Newcastle on Sunday.
It brings to an end an almost two-month process to find a permanent successor to Graham Potter, who was sacked on April 2.
The PA news agency understands Pochettino had been the club’s first choice from early in the search, which was led by co-sporting directors Paul Winstanley and Laurence Stewart.
He was the only candidate the club got into serious talks with, despite conversations that took place with former Bayern Munich boss Julian Nagelsmann, ex-Spain coach Luis Enrique and Burnley’s Vincent Kompany.
The new manager, whose contract includes an option for a third season, will work closely with Winstanley and Stewart as the club look to rebuild after their worst season in 30 years.