The 26-year-old has signed a three-year-deal with the Hammers and will link up with the Barclays Premier League side when his current contract at Betis expires at the end of the month.
Adrian will challenge experienced goalkeeper Jussi Jaaskelainen to be Sam Allardyce's first-choice at Upton Park for next season.
Adrian will end a 16-year affiliation with Betis to move to East London and he is looking forward to a new challenge in his career.
"I am extremely happy and ecstatic to have joined such a legendary and historical club in both London and in England," he said. "I am really looking forward to being able to kick-off my career in the best league in the world with West Ham.
"I started off my career as a 10-year-old and have been there all of my life. I came through the ranks and I made my first-team debut in the sixth league game of last season against Malaga and was an ever-present since."
Jaaskelainen established himself as the firm number one at West Ham last season after being signed by Allardyce ahead of the club's return to the top-flight.
Adrian will now look to challenge for the position but is looking forward to working alongside the experienced Finn to develop his own game.
"I am very fortunate to be able to work with such an experienced goalkeeper with such a long track record in the Premier League as Jussi Jaaskelainen," he added.
"I'm really looking forward to working with him on a daily basis and being able to receive tips from him which I'm certain will make me an even better goalkeeper."
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- Sam Allardyce