The 20-year-old free agent has penned a two-year deal with Wanderers and becomes new manager Stale Solbakken's second summer signing after that of fellow forward Bjorn Sigurdarson.
Nouble started his career with Chelsea before joining the Hammers in 2009, although he has made just 19 appearances in his three years at Upton Park, scoring once.
He has, however, gained a host of experience during loan spells with Black Country rivals West Brom, Swindon, Swansea, Barnsley, Charlton, Gillingham and a second spell with the Tykes.
Solbakken told Wolves' official website: "Frank is a player who our scouts have been watching. We think he has qualities we can develop and with his physical strength and power, I feel he can help us. He should be a useful acquisition to the squad and it is a good opportunity for him to come to a stable club and work hard.
"I think this is a win-win situation for both the club and the player. He is a young guy and he can add to his potential every week."