"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."
The Best Song Ever hitmakers will record their fifth album in Malik's absence and will continue with the remaining dates on the band's forthcoming world tour.
One Direction said in a second statement: "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."
Meanwhile, Simon Cowell - who masterminded One Direction from five solo artists who auditioned for The X Factor back in 2010 - thanked Malik for his commitment to the band.
He added: "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."
Within minutes of the news being announced, the star's name was trending on Twitter as the heartthrob's fans mourned their pop idol's departure.
Reactions ranged from heartbroken, to compassionate to angry, but the overriding emotion was devastation.
Some fans questioned whether the others could continue on as a four piece without Zayn.
Even famous stars joined in to share their thoughts on the news as Piers Morgan and Katie Hopkins tweeted their reactions.
Last Thursday, Zayn left One Direction's On The Road Again tour prematurely - abandoning band mates Harry, Louis, Niall and Liam - when he was accused of cheating on his girlfriend of three years.
A spokesperson for the band said: "Zayn has signed off with stress and is flying back to the UK to recuperate. The band wish him well and will continue with their performances in Manila and Jakarta."
He was holidaying in Phuket with fellow band member Louis when he was pictured holding hands and with a 19-year-old girl, Lauren Richardson, last week.
Two pictures, including one that saw Zayn resting a hand on the same girl's midriff in an embrace and another of him leaving the Seduction nightclub with the girl, quickly went viral on social media.
As a result flew straight home for "crisis talks" with girlfriend Perrie Edwards, who he has been engaged to just over a year.
Malik tweeted about the most recent incident to publicly apologise for "what it looked like" and declare his love for the Little Mix singer, shortly after the incriminating pictures surfaced.
"I'm 22 years old ... I love a girl named Perrie Edwards. And there's a lot of jealous f**** in this world. I'm sorry for what it looks like," he wrote.
The father of Lauren Richardson - the tattooed blonde at the centre of the recent cheating scandal - described Malik's shock decision to quit the band for good as the "worst case scenario".
Speaking at Richardson's family home in Walthamstow, east London, David Richardson suggested his daughter had gone in to hiding and declined to say where she was.
He said: "Lauren's not in, you can imagine the attention we've had. I got that good news when I got home from work. It's the worst scenario.
"I've got nothing to say on the matter whatsoever and, as you can imagine, all we want is to be left in peace."
The singer and his fiance spent five hours talking at the house that they shared, with Perrie leaving without her engagement ring and with her bags packed.
The One Direction holiday sparked a second scandal on Sunday morning when pictures of Louis Tomlinson kissing a girl in a pool emerged and rocked his four-year relationship with Eleanor Calder, which is now thought to have ended.
Four piece Harry, Louis, Liam and Niall continued with the Asian leg of the 1D tour though the band sparked criticism when Liam jokingly covered up Malik's face on a poster.
Malik was thought to be the most reluctant member of One Direction from the start.
He first auditioned as a solo singer on The X Factor in the summer of 2010, but his mum admitted in 2013 that he was reluctant to audition.
"He hated dancing but loved singing," she recalls. "He used to sing until three o'clock in the morning and I often used to have to ask him to turn it down."
The family - Malik's parents, three sisters and the family dog - have moved to a new house in the city which was bought by Malik.
In the recent One Direction movie, Trisha is seen, overcome with emotion, as she is handed the keys.
"We never had enough money to buy our own house," she explains. "We always lived in rented accommodation, so Zayn knew how very important it was for me to have my own place."
Last year saw Malik hit back against drug abuse claims made about him by US host Matt Lauer on The Today Show in November.
Speaking to The Sun, he fumed: "I'm really angry and upset by what was said on The Today Show. I was really ill at the weekend. That's why I couldn't fly to America."
When Lauer interviewed the boys, he shocked them when he asked if Zayn's absence was related to drugs.
Liam replied: "No, he's just got a stomach bug. He's okay. He's just at home. He just needs to rest."
DID YOU MEET ZAYN WHEN THEY TOURED IN NEW ZEALAND? EMAIL US HERE
- Daily Mail
