Henderson loaned to Hammers
Manager Sam Allardyce has snapped up the 23-year-old Irishman until the end of the season with a view to a permanent switch in the summer.
Henderson will initially provide cover for Hammers number one Robert Green, who is out of contract at the end of the season.
“I’m sad to leave Portsmouth but very happy to join a successful club in West Ham,” said Henderson.
Henderson is the fourth player to leave Pompey after they slid into administration last month, with top scorer Erik Huseklepp joining Birmingham, captain and fellow Irish international Liam Lawrence moving to Cardiff and midfielder Hayden Mullins signing for Reading.