The Hammers had a £40m offer accepted by Wolves on Friday and he passed his medical this morning.
The 27-year-old has put pen to paper on a seven-year contract at London Stadium.
“It’s an amazing feeling to be a West Ham United player,” said Kilman.
“As soon as I was aware of the interest from the Club, it was an opportunity I was keen to pursue, so I couldn’t be more delighted to be here.
“I really enjoyed working with Julen (Lopetegui) during his time at Wolves – he’s a top-class coach and someone I learned a lot from, and I am confident I will continue to improve as a player under his management here.”
Kilman added: “West Ham is a massive Club and I feel this is the natural next step forward in my career.
“Playing in front of a passionate fan-base, with 62,500 supporters packing out London Stadium every other week, is something I am incredibly excited about.
“Having spoken at length to both Julen and Tim (Steidten), I was hugely encouraged about the ambition of the Club and their plans for the future. They want to make a big noise here at West Ham and as a new player coming in, that’s an incredible thing to hear.
“I’m looking forward to getting down to work and preparing for an exciting season ahead.”