Watts, who featured for Eddie Howe's first team at the start of pre-season, will stay with Grant McCann's men - who currently sit fourth in the third tier - until the next transfer window.
The 22-year-old was part of the Wigan Athletic side that won League One last term, with the centre back making 35 appearances as he established himself in a successful spell at the DW Stadium.
He has also spent time out on loan at Stevenage, Mansfield Town and Plymouth Argyle in recent seasons, and made his competitive Magpies debut in the Premier League defeat to Liverpool in July 2020.
The former England Under-19 international could make his bow for the Posh in Saturday's League One game at Portsmouth's Fratton Park.