The 21-year-old centre-back has signed a five-year deal with the London club. Though the Hammers did not disclose the fee, BBC Sport reports the price paid was £22 million.
Diop told the club's website: "Manuel Pellegrini is a top coach who has worked at some huge clubs around the world. I'm looking forward to working with him and showing him what I can do.
"I am a very ambitious player and West Ham is a very ambitious club, as we've seen with the appointment of the new coach. I hope to help the team win lots of games and make the fans happy."
Diop had been attracting the attention of several European clubs on the back of strong performances in Ligue 1, and his signing is an indication of the level on which West Ham wants to compete in the transfer market under new manager Pellegrini and new director of football Mario Husillos.
Husillos said: "Issa is a player with fantastic potential who has already shown great quality at such a young age. There were many other big clubs interested in signing Issa and we are delighted that he has chosen to join us."
He enjoyed his most successful individual season to date last term, starting 34 league matches and scoring three times.
The France under-21 international becomes West Ham's second signing of the summer after Fulham right-back Ryan Fredericks. The club is also thought to be close to adding goalkeeper Lukasz Fabianski from relegated Swansea City.