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 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.
Zayn's had a tumultuous time with the band and almost quit during bootcamp.
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Border policing command deputy director Tom Dowdall said a fresh intelligence-gathering campaign was being launched.
He said the threat around Essex, Kent and Sussex from migrants reaching the UK in small boats needed attention.
MPs have raised concerns about a lack of Border Force boats to patrol the coast.
The Home Affairs Select Committee said only three boats were available to patrol 7,000 miles of shoreline. The Home Office said it made use of radar and aerial surveillance and has ordered eight more boats.
In the latest incident, Sussex Police arrested five men at Winchelsea after a group arrived on a dinghy.
Police said the group, all from Iran, were held on suspicion of gaining illegal entry to the UK on Sunday and are now being dealt with by the Home Office.
Mr Dowdall said: "We will, with Border Force, be re-launching a community-intelligence gathering over the course of this summer.
"What we ask people to look out for is what out there did they consider to be abnormal.
"We certainly think that the threat that's posed in the south coast... requires some more focused attention with the local communities, which we think will be very helpful to us."
Zayn Malik has quit One Direction, the band have confirmed in a statement.
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Community intelligence is needed to tackle the migrant boat threat along the south coast, a National Crime Agency (NCA) chief has said.