The 30-year-old, who was part of the Argentina squad which won the World Cup in 2022 and the 2021 and 2024 Copa America titles, was available on a free transfer following the expiry of his contract at Real Betis.
Rodriguez spent the last four-and-a-half years in Spain, becoming a key player as Betis have qualified for European football in each of the past four seasons.
“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," Rodriguez said in a club statement.
"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."
The Hammers have already added German international striker Niclas Fuellkrug, wingers Crysencio Summerville and Luis Guilherme and defender Max Kilman to their squad for Julen Lopetegui's first season in charge.
Technical Director Tim Steidten said Rodriguez's signing was a "statement of intent" as they aim to improve on finishing ninth in the Premier League last season.
“This is a massive moment for West Ham United in bringing a player of Guido’s pedigree to the club," said Steidten.
"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."
