Malik said: "My life with One Direction has been more than I could ever have imagined. But, after five years, I feel like it is now the right time for me to leave the band.
"I'd like to apologise to the fans if I've let anyone down, but I have to do what feels right."
One Direction will continue their world tour as a four piece and record a fifth album later this year.
Last week, Malik walked away from the band's world tour last week after being signed off with stress.
He returned to the UK shortly after being forced to defend his relationship with his fiancee, Little Mix singer Perrie Edwards.
A photo had earlier emerged of him holding another woman around the waist.
A second photo, taken from behind, showed Malik standing close to the woman. Their hands and arms looked as though they were linked.
In a statement, the rest of the group said: "We're really sad to see Zayn go, but we totally respect his decision and send him all our love for the future.
"The past five years have been beyond amazing - we've gone through so much together, so we will always be friends.
"The four of us will now continue. We're looking forward to recording the new album and seeing all the fans on the next stage of the world tour."
Simon Cowell, who discovered the boyband on talent show The X Factor, said: "I would like to say thank you to Zayn for everything he has done for One Direction.
"Since I first met Zayn in 2010, I have grown very, very fond - and immensely proud - of him. I have seen him grow in confidence and I am truly sorry to see him leave.
"As for One Direction, fans can rest assured that Niall, Liam, Harry and Louis are hugely excited about the future of the band."
Niall Horan, Liam Payne, Harry Styles and Louis Tomlinson signed with Simon Cowell's record label Syco Records in 2010 after finishing third on The X Factor.