The 29-year-old was the subject of a late move on deadline day from the Canaries, who managed to get their statement of intent, with all relevant signatures, to the Premier League prior to the 6pm cut-off.
Jarvis has featured eight times already for West Ham this season, but the Hammers signed the likes of Victor Moses and Michael Antonio on September 1, pushing Jarvis further down the pecking order.
Jarvis has scored six times in 90 matches for the East London club, having signed from Wolves for a then club-record fee of £10.75m in 2012.
And Jarvis has caps for England, featuring in the 2011 friendly against Ghana at Wembley.
He began his career at Gillingham, where he played 122 times prior to beginning a five-year spell at Molineux in the summer of 2007.