Kilman has joined the Irons on a seven-year contract in a £40m deal.
Steidten told the club's website: “We’re delighted to have secured Max’s signature – he was one of our top targets in the central defensive area in this transfer window, so we couldn’t be happier to have completed the deal to bring him to West Ham United.
“This is a serious and notable moment for West Ham United – the signing of an established, proven English Premier League central defender in the peak years of his career.
“He has many great qualities as a defender. He’s a strong, powerful centre-back, who possesses the leadership qualities that are so important in that area of the pitch.
“Julen (Lopetegui) and I have spoken at length about the kind of characters we want to bring to West Ham, and Max fits the bill.
“His arrival shows the ambition of the Board to bring big players to the Football Club. I’m sure the West Ham fans are as excited as we all are about this signing.”