The couple said that no one else was involved in their break-up, which comes after 11 years of marriage, during which time they had two daughters.
Jopling owns the White Cube Gallery, with artists including modern art headliners such as Damien Hirst and Tracey Emin, while Taylor-Wood is best known for a video portrait of David Beckham sleeping.
"Jay Jopling and Sam Taylor-Wood are saddened to announce that, after 11 years of marriage, they have agreed amicably to separate," said White Cube gallery spokeswoman Sara Macdonald.
"No other parties are involved.
"For the sake of their two daughters, who are their number one priority, they have asked that their privacy be respected."