The 20-year-old joined the south-coast club from Chelsea in 2021 for £5m.
Livramento's departure comes after Southampton were relegated from the Premier League last season.
The England Under-21 defender made just two outings last term after suffering an anterior cruciate ligament injury in April 2022.
He came on as a substitute in Southampton's final two games of campaign against Brighton and Liverpool.
Livramento played 32 games during the 2021-22 season, 28 of those in the Premier League.
Newcastle have signed Italy midfielder Sandro Tonali and England winger Harvey Barnes this summer as the Tyneside club look to push on from their top-four finish last season.