The Israeli has signed a four-year deal with the Hammers to succeed Gianfranco Zola as the top man at Upton Park but will need to be granted a work permit before the deal is final.
Despite that, the man who took embattled Pompey to the FA Cup final last season, was excited about his new challenge with West Ham.
"I'm proud and honoured to be the manager of West Ham. It's an exciting challenge and I'm ready to do my best," Grant told the club's official website.
"West Ham is a fantastic club with great fans and a history that is respected around the world.
"I'm already looking forward to getting to work with my players in July and preparing for the new season."