The 23-year-old centre-back, who featured for Eddie Howe's side at the beginning of pre-season last summer, joined the Posh on loan in September until January but will now remain at the London Road Stadium until the end of the current campaign.
Watts, who made his Premier League debut for his boyhood club on the final day of the 2019/20 season against Liverpool at St. James' Park, spent last term on loan at Wigan Athletic and won the League One title, making 35 appearances for the Latics.
The former England Under-19 international also completed loan stints at the likes of Stevenage, Mansfield Town and Plymouth Argyle in recent seasons and made his 100th English Football League appearance on New Years' Day against Wycombe Wanderers.
Darren Ferguson's side currently sit in eighth place of the English third tier, five points adrift of the play-off spots.