The 22-year-old, who joined the Magpies from Northampton Town in 2015, managed just two Premier League and two EFL Cup appearances for the club.
After being sent out on loan to Barnsley, Shrewsbury Town, Scunthorpe United and Wigan Athletic, Toney has now taken the chance to leave for League One side Peterborough on a permanent basis.
Darragh MacAnthony (@DMAC102) August 9, 2018
The fee is undisclosed, but Posh owner Darragh MacAnthony revealed on Twitter that it is a "substantial six-figure deal".
Toney scored 14 goals in 46 appearances across spells with Wigan and Scunthorpe last season.