The Devils announced the move on Thursday, the day before the start of the NHL's free-agency period.
The 34-year-old Schneider has two years remaining on the seven-year, $42 million contract. He was to be paid $6 million annually the last two seasons. The buyout is $8 million spread out over four years.
The buyout is two-thirds of the total of the amount left on the contract and it is is spread out over twice the length remaining on the deal.
Schneider, who had hip surgery after the Devils made the playoffs in the 2017-18 season, has struggled the past two years.
The Massachusetts native posted a 3-6-2 record with one shutout during the COVID-19-shortened regular season, part of which he spent at Binghamton of the AHL because of poor play. He played in only 26 NHL games the season after his surgery.
The Devils will probably have to use the free-agent market or make a trade to find a backup for Mackenzie Blackwood. The 23-year-old established himself as the team's No. 1 goaltender this past season, posting a 22-14-8 record with a 2.77 goals-against average and three shutouts.
The Devils acquired Schneider from Vancouver in a draft-day deal in June 2013. Schneider split the goaltending duties his first season in New Jersey with Hall of Famer Martin Brodeur. He took over the No. 1 role the following year, finally leading New Jersey back to the postseason in 2017-18 with Taylor Hall.
Keith Kinkaid played well down the stretch in 2018 and was the Devils' top goaltender coming into the playoffs. Schneider, who also battled a groin injury, took over and played well in the final three games in an opening-round loss to Tampa Bay.
Schneider has a 170-159-58 record with a 2.43 goals-against average in his career. His best season was in 2015-16 when he posted a 27-25-6 record with a 2.15 GAA and four shutouts on a very bad New Jersey team.