Diop has made a big name for himself in his homeland, having racked up just short of 100 appearances for Toulouse since breaking into the first team at the age of 18.
New West Ham boss Pellegrini is excited by the qualities Diop can bring to the side, telling United's official website: "Issa is a defender with great talent and character.
"He is only 21, but he has already established himself as a key player over a period of time with Toulouse. We believe he has defensive qualities that will be well suited to the Premier League - pace, power and a sharp concentration - and I also feel he will complement the other central defenders we have.
"We know that many other top clubs in England and Europe were keen to sign him, so it was important that we moved quickly to complete the deal."