The 20-minute footage featuring the American rock band taking to the road with US comedian Ken Jeong, was shared with fans on Facebook.
A script at the beginning of the video says: “With the blessing of Chester’s family and his bandmates, we share this episode and dedicate it to the memory of Chester”.
The video, which sees the band driving around LA singing a selection of their own hits as well as covers, was recorded in LA on 14 July - six days before the singer took his own life.
Story continues after the video...
The 41-year-old was found dead at his home in Palos Verdes, LA, on 20 July.
Carpool Karaoke is a spin-off web series of the popular segment on ‘The Late Late Show’, originally featuring James Corden.
The segment has seen many of the biggest names in music, including Adele, One Direction, Madonna and Justin Bieber, accompany the host as he drives around LA while singing along to their hits.
Earlier this year, Apple Music launched a new feature length version of the series with different celebrities standing in for the British actor and preseneter, who serves as executive producer.
Following the news of Chester’s death, James Corden told the Associated Press: “We will approach it in whichever manner his family or the people that were involved in that episode, however they would like it to be handled.
“We will navigate it as delicately as possible and just adhere to whatever wishes they would want because I don’t think there’s any other way we could deal with it.”