West Ham, who finished one place above the relegation zone last season, sacked Gianfranco Zola in May after almost two seasons in the job.
New co-owners David Gold and David Sullivan have now turned to the 55-year old former Chelsea and Israel boss Grant to restore their fortunes.
"I am delighted to welcome Avram to West Ham and am confident he will prove a success. We have taken our time over this appointment and are certain we have got the right man," Sullivan told the club website.
Grant, who has signed a four-year-contract at Upton Park, finished the last campaign with many admirers in the game for his dignity in a chaotic season at cash-strapped Portsmouth.
"I am proud and honoured to be the manager of West Ham. It will be an exciting challenge and I am ready to do my best," Grant said in a statement.
"This is a fantastic club with great fans and a history that is respected around the world. I am already looking forward to getting to work with my players in July and preparing for the new season."
West Ham used to be known as one of the most stable clubs in English football and it is their proud boast that they had only five managers in their first 87 years.
However, recent times have proved far more turbulent at the club with changes of ownership and a high turnover of managers - Grant is the sixth in the last nine years.
NEW BROOM
Gold and Sullivan became the new joint-owners in January and quickly gave a public airing to their disappointment with Zola and the team's performances.
The Italian had taken West Ham to ninth in his first season as a full-time manager but struggled last season, managing just eight league wins.
"We needed experience and stability. He is a footballing man and quite frankly his reputation speaks for itself. He has a great sense of humour and I am sure the players will relate to him and the fans will warm to him," Gold added.
Grant began his managerial career in Israeli club soccer before taking charge of his national team for four years from 2002.
He moved to England to become technical director at Portsmouth and, after a brief spell as director of football at Chelsea, succeeded Jose Mourinho as manager there in September 2007.
He steered Chelsea to the runners-up spot in the Premier League and lost the Champions League final to Manchester United on penalties, and was immediately sacked having served eight months of a four-year contract.
He returned to Portsmouth as director of football in October 2009 and a month later replaced Paul Hart as manager.
During a nightmare season, Portsmouth went into administration with debts of around 119 million pounds, were docked nine points by the Premier League and finished bottom of the league.
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