The group said they would continue as a four-piece for their world tour and record another album — their fifth — later this year.
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 in my heart.
“I am leaving because I want to be a normal 22-year-old who is able to relax and have some private time out of the spotlight. I know I have four friends for life in Louis, Liam, Harry, and Niall. I know they will continue to be the best band in the world.”
Malik quit the boyband’s world tour last week after being “signed off with stress” and returned to the UK after he was forced to defend himself online and declare his love for fiancee Perrie Edwards when pictures emerged of him apparently close to another woman.
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.”
A spokesman for the band said Malik, who grew up in Bradford, is at home with his family and fiancee — Little Mix singer Perrie Edwards.
Simon Cowell, who discovered the boyband on 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.”
Malik appeared in a leaked video last year smoking what appeared to be a joint while the group travelled in a van in South America. He was also forced to explain his absence from promotional commitments after a US television host questioned his bandmates about ”rumours of substance abuse”.
One Direction are set to continue on their world tour this year, playing South Africa in the next week before returning to Europe and North America in the summer.