The Mexican midfielder has signed a five-year contract at the London Stadium.
West Ham have paid £35m for the 25-year-old, who will wear the number 19 jersey.
Alvarez will come in as a replacement for Declan Rice after the Englishman joined Arsenal for £105m earlier in the transfer window.
"It's a hugely sentimental moment for me in my career - it is a dream for me and my family," Alvarez said.
"The Premier League is a special league, the best league in the world and I think my style will suit it.
"I now have a responsibility to West Ham and the West Ham family and I will give absolutely everything for the shirt."
Manager David Moyes added: "We're really pleased to add Edson to our squad. The midfield area was one we were especially keen to strengthen this summer - and Edson will complement the other options we have in that department.
"He's an experienced international player, who has enjoyed great success for both club and country during his career to date."
Alvarez spent four years with Ajax and won the Dutch Eredivisie twice.
He has won 68 caps for the Mexico national team, helping them win the CONCACAF Gold Cup last month.
West Ham are also set to complete deals for Manchester United defender Harry Maguire and Southampton captain James Ward-Prowse.
