The Premier League club have been looking to add a striker to their squad and have decided to smash their club-record transfer to land the Sweden international.
Spanish outlet El Diario Vasco were the first to report the story, and sources have told ESPN that the LaLiga club are already looking for his replacement.
Isak joined Sociedad in the summer of 2019 from Borussia Dortmund for €10m and, after spending four years at the club, becomes Sociedad's most expensive departure of all time.
Sources also added that the Isak deal includes Sociedad retaining 10% of any future departure.
The LaLiga club were always aware of potential interest in the striker and increased the release clause in his contract to €90m in late 2021.
Sociedad have agreed to a reduced fee from Newcastle as the offer was too good to turn down, and it was also based on the player's performance last season, when he had only six goals from 32 league appearances.
However, the striker has been a key part of Sociedad's forward line over the past few seasons with 44 goals in 132 matches.
In February 2021, ESPN reported that Barcelona were closely monitoring Isak's development, and during the January transfer window the striker was also linked to other Premier League clubs, including Arsenal.