The 22-year-old forward has passed a medical at London Road and has agreed terms on a move to the Posh.
Manager Nathan Jones said: “We’ve accepted an offer for Jack that enables the club to move forward.
“We identified that he had frustrations last year with the amount of game time he had and with the quality of front men that we have, we couldn’t hold Jack back.
“It’s a good deal all-round for the club and ourselves, and with the ones we are bringing in, we feel that we’ve improved the squad and have been able to move the club forward.
“I couldn’t fault Jack’s attitude and work-rate. It’s just the competition we had here was so strong that we felt it was the right thing for all parties and we wish him well.”
Marriott leaves the Hatters with a record of 28 goals in 91 appearances during his two seasons at Kenilworth Road since signing from Ipswich Town in the summer of 2015.
Marriott, who had impressed against the Town in the Conference during loan spells with Woking, netted 16 times in his debut season, earning the supporters’ player of the year award and a new three-year deal before the start of 2016-17.
He reached double figures again last term, registering 12 goals in 29 starts and 18 substitute appearances to finish third top scorer behind Danny Hylton and Isaac Vassell.
Town chief executive Gary Sweet added: “Jack was unfortunate that he didn’t get more of an opportunity last season due to the form of others, and we are confident that he will continue to develop at Peterborough. It’s a good move for him.
“We are happy with the deal, otherwise we wouldn’t have parted company with such a good player unless we felt that the funds coming in wouldn’t strengthen the squad overall.
“We thank Peterborough for their professionalism and we hope he cracks on with them. Following the sale of Cameron McGeehan, we are all Peterborough and Barnsley fans now and want the players to do well. We all wish Jack well for the future.”
All at Luton Town Football Club would like to thank Jack for his contribution at Kenilworth Road over the past two years and wish him every success in his career.