"It is with great sadness and eternal admiration that we report the passing of [a] rock and roll icon," read a statement on his official website.
McLagan, known as Mac, played on such memorable Small Faces tracks as Lazy Sunday and Itchycoo Park in the 1960s.
The band became the Faces when Rod Stewart and Ron Wood joined in 1969.
McLagan went on to record and perform with the Rolling Stones and also worked with Chuck Berry, Bob Dylan and Bruce Springsteen.
The Hounslow-born musician was about to embark on a North American tour, supporting label mate Nick Lowe, at the time of his death in his adopted home town of Austin, Texas.
"I am completely devastated by this shocking news and I know this goes for Ronnie and Rod as well," said Small Faces and Faces member Kenney Jones.
Steward added: "I'm absolutely devastated. Ian McLagan embodied the true spirit of the Faces.
"Last night I was at a charity do, Mick Hucknall was singing I'd Rather Go Blind, and Ron Wood texted to say Ian had passed. It was as if his spirit was in the room. I'll miss you mate."
McLagan's manager, Ken Kushnick, remembered him as "a beloved friend to so many people and a true rock 'n' roll spirit".
As a member of Small Faces, McLagan was known for his dexterity on the Hammond Organ and Wurlitzer electric piano.
With the Faces in the 1970s, he had hits in both the UK and US with such songs as Stay With Me and Cindy Incidentally.
When Stewart departed to go solo and Wood left to join the Stones, the group continued as the Small Faces, before disbanding in 1978.
The Faces reformed at the end of the 2000s, with Mick Hucknall filling in for Stewart, and were inducted into the Rock and Roll Hall of Fame in 2012.
According to the announcement on his website, McLagan had a stroke on Tuesday and died the following day "surrounded by family and friends".
Singer Billy Bragg tweeted that "British rock has lost one of its greatest players", while Hucknall paid his own tribute on the Simply Red twitter feed.
"Ian McLagan will not be resting in peace," the band's message read. "He'll be rocking whichever house he chose to be in. Bless his soul."
