The centre-back has penned a four-year contract with the Premier League outfit.
Ogbonna, who has 10 international caps, made 31 appearances for Juve last season and was an unused substitute in the Champions League Final.
He joined the Italian champions from city rivals Torino in 2013.
The 27-year-old is the Hammers' fifth summer signing, after Pedro Obiang, Dmitri Payet, Darren Randolph and Stephen Hendrie.