The Argentina international joins as a free agent after coming off contract last month.
“I’m very happy to be here,” Rodriguez told whufc.com. “I feel like it’s every footballer’s dream to play in the Premier League, and I was very excited when I heard that West Ham were interested in me.
“It’s a historic Club, that has a really interesting project. I think it’s the right Club for me, at the right time, and I hope together we can keep growing. I spoke to Edson (Álvarez) before signing, and we’re both really looking forward to working together again.
“I will help the team in any way I can. I will bring experience to the team, and though I’m aware the Premier League is very physical, I’m ready to put the work in to make sure I’m up to the task.
“What I can say to the fans is that I will give them everything. I’m very motivated, and I think together with the supporters we can achieve many good things. I just can’t wait to get going now!”
Technical Director Tim Steidten also stated: “This is a massive moment for West Ham United in bringing a player of Guido’s pedigree to the Club. He is a player I have admired for a long time, and we couldn’t be happier to have completed the deal to bring him to east London.
“Guido is a defensive midfielder whose intelligence in and out of possession is a real strength to his game. He is also a proven winner, having won the World Cup, Copa América and Finalissima with Argentina, so to have secured his services is a big statement of intent by the Club.
“We feel it is important to strike a balance between youth and experience across the squad, and adding a player with the experience and leadership qualities of Guido will be a real asset to the Club moving forwards.
“It’s a busy period in this transfer window, and the Board are continuing to show they’re backing us to bring quality players to West Ham United.”