In a statement posted on Iron Man star Paltrow's Goop.com website under the headline "Conscious uncoupling", they said they had made the decision "with hearts full of sadness".
Chris Martin and Gwyneth Paltrow
The couple, who married in 2003, have two children together, daughter Apple, nine, and son Moses, seven.
In a statement signed "Gwyneth and Chris", they said: "We have been working hard for well over a year, some of it together, some of it separated, to see what might have been possible between us, and we have come to the conclusion that while we love each other very much, we will remain separate.
"We are, however, and always will be a family, and in many ways we are closer than we have ever been.
"We are parents first and foremost, to two incredibly wonderful children and we ask for their and our space and privacy to be respected at this difficult time.
"We have always conducted our relationship privately, and we hope that as we consciously uncouple and coparent, we will be able to continue in the same manner."
Paltrow won an Oscar in 1998 for her role in Shakespeare In Love. Most recently she has appeared in the three Iron Man films.
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