Jenkinson has struggled to break into the first team at the Emirates Stadium since joining from Charlton Athletic in 2011, and will now hope to impress with his performances at Upton Park.
The chance for regular first-team football convinced the defender, who has one England cap, to make move the across London and become Sam Allardyce's sixth close-season signing.
"I'm clearly seen as a big part of things here and hopefully I can prove my worth here because it is an important year for me," the 22-year-old told the club's official website.
"I was flattered to have a lot of options but, deep down, if I was being honest with myself West Ham was always the place I wanted to go to.
"It's one of them where I wanted to do the right professional thing and consider all the options, but in the back of my mind it was always West Ham and I'm just so glad it's all worked out how I wanted it to in the end.
"It's a very exciting time to be a part of this club.
"There is an English group of lads here, which is always great for an English lad, and the players who have been brought in are top-drawer, so there is every reason to be optimistic about this season.
"That was a big reason I signed here."
Jenkinson made 14 Premier League appearances last season as he spent the campaign as back-up to Bacary Sagna, who has also left the club for Manchester City.
Rather than look to Jenkinson to fill that gap, Arsene Wenger has added Newcastle United's Mathieu Debuchy and Southampton's Calum Chambers.
