Parkinson has signed a deal to 2028 with the Bairns and moves for an undisclosed fee.
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The 20-year-old, who joined the Magpies' Academy aged seven, progressed through the club's youth system and signed his first professional contract in 2023.
He made his Premier League debut later that year, featuring as a second-half substitute against Bournemouth at the Vitality Stadium.
The Durham-born forward scored eight goals in 11 Premier League 2 appearances last season, as well as netting against Bradford City in the EFL Trophy.