Lightbody, 47, said that he and the other the other band members, Nathan Connolly and John McDaid, were “heartbroken” but would remain in the band and continue to work on their next album together.
Snow Patrol was formed by Lightbody in 1994 in Dundee, Scotland, adding Quinn in 1997 and Wilson in 2005.
Sharing the news on the rock band’s official Instagram account, Lightbody wrote: “Hi everyone, sorry to be the bearer of such sad news but both Jonny Quinn and Paul Wilson have decided to leave Snow Patrol.
“We are heartbroken they have decided to leave us but we wish them nothing but happiness, success, joy, compassion and everything they want in all their future endeavours.
“This first post is purely to let you all know what’s happening. The next two posts will be dedicated to Jonny and Pablo separately as they deserve to each have a proper and individual send off.
“Nate (Connolly), JMD (McDaid), and myself will continue with SP (Snow Patrol) and there will be a new album next year but more news of that will come at an appropriate time, for now we want to pay homage and give gratitude for all Jonny and Pablo (Paul) have given us and shared with us these past decades. Love to Jonny and Pabs, and love to you all.”
A further two Instagram posts were uploaded to Snow Patrol’s Instagram, one dedicated to Quinn and one to Wilson.
Writing about drummer Quinn, 51, Lightbody said: “Jonny joined the band in 1997 and therefore, other than myself, has been in the band longer than anyone.
“26 years is a hell of a long time to do anything and we are so glad he decided to spend all that time with us.
“Early on it was clear he was more than a drummer.
“His background, as well as drumming, was in band management and gig promotion in Belfast and he has taken on the role of manager for us many times during the last quarter century.
“From driving his car with all our gear in it, to our first gig forays outside of Dundee where it all started for us (including saving all our lives with some quick thinking/great driving when we nearly span out of control off an icy bridge in Perth), to having to be the grown-up in the room many times in the early days when we were green and cutting our teeth, he was a steady hand when we needed one, and a ferocious defender many times too.”
He added: “To be continuing without him after all this time is very strange and sad as he has been a constant presence in our lives.”
Lightbody also wrote about bassist Wilson, 44, and said: “Paul officially joined the band as a bassist in 2005 just before the making of Eyes Open but he had been a live member of the band on guitar for years before that.
“The band he was in previous to SP was Terra Diablo and they toured with us many times and Pablo would play their set and then jump on with us and play ours too.
“I remember those early Terra Diablo shows, him climbing on speakers and jumping off things that were way too high to jump off.
“One very memorable night in King Tuts, Glasgow he hung upside down from the rafters and played a guitar solo. He had no fear. It was thrilling to watch.”
He added: “Thank you for all the awesome times you’ve given us and shared with us Pabs.”
He also said that the band could not wait to hear his new music with Above As Below.
Additional reporting from the Press Association