The musician announced his split from Rachel Owen after 23 years together.
In a statement to NME, Thom said: ''Rachel and I have separated. After 23 highly creative and happy years, for various reasons we have gone our separate ways. It's perfectly amicable and has been common knowledge for some time.''
The couple have two children together, Noah and Agnes. They met at the University of Exeter where Rachel studied fine art printmaking.
Radiohead are currently at work on their ninth studio album, which guitarist Jonny Greenwood admitted ''took a lot of time'' to come to fruition.
He said in June: ''We didn't do anything together for too long, so restarting took a lot of time.
''We're working in periods now. This afternoon, Thom [Yorke] and I will work on a song we started yesterday, see what it will lead to.''
Jonny previously revealed the 'Paranoid Android' rockers have ''change their method'' and were experimenting with different things in recording.
He said: ''We've certainly changed our method again. It's too involved [to explain how].
''We're kind of limiting ourselves; working in limits. So we'll see what happens. It's like we're trying to use very old and very new technology together to see what happens.''
American Thighs was released on this day in 1994.