The pair last night announced the end of their 10-year marriage - which they termed "conscious uncoupling" - after ongoing rumours that there were divisions in their relationship.
They said in a joint statement posted online that they had been trying to work through their problems both together and individually. But the couple - who have two children - added: "We have come to the conclusion that, while we love each other very much, we will remain separate."
Paltrow and Martin - who met when she was already a major star and Coldplay were still making a name for themselves on the world stage - have always tried to shun publicity about their relationship.
They were rarely pictured together in public and he was reluctant to acknowledge in interviews that he was married to an Oscar-winning actress. If they did venture out together, they would shy away from cameras.
The couple, who married in December 2003, have two children together - daughter Apple, nine, and seven-year-old son Moses. For many years they were based in London, where the children went to school, but then uprooted to Los Angeles last year, although they had talked about returning.
In a statement posted on Iron Man star Paltrow's Goop.com website under the headline "Conscious uncoupling", the 41-year-old actress and Martin, 37, 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 co-parent, we will be able to continue in the same manner."
Their statement also featured an Instagram-style picture of the couple dressed smartly but sitting on a lawn. Beneath it is a lengthy article about "a new way of being in relationships", written by a regular contributor to Paltrow's lifestyle website, together with a homeopathic children's dentist.
It says: "The idea of being married to one person for life is too much pressure for anyone."
The post - signed by "Gwyneth and Chris" - was enough to crash the site as visitors attempted to view it.
Despite their reluctance to appear together, they did accompany each other at some public events earlier this year - the Golden Globes in Beverly Hills and the Help Haiti Home gala.
Paltrow, who won an Oscar in 1998 for her role in Shakespeare In Love, has continued to maintain her film career with appearances in three Iron Man movies in addition to holding down her family life and running her website.
Martin is just about to enter another busy stage of his career with the release of Coldplay's sixth album, Ghost Stories, in May, and there will be expectations of a tour to promote the new songs. The band have already given the tracks a live airing, at the SXSW festival in Texas earlier this month.