The Swedish international flew to Tyneside on Thursday after the two clubs agreed a fee believed to be in the region of £60million earlier this week.
After undergoing a medical, the 22-year-old officially became the Magpies record signing on Friday afternoon, surpassing the £40million move that brought Joelinton to St James Park from German club Hoffenheim three years ago.
Isak enjoyed a productive three-year spell with the La Liga club, scoring 44 goals and providing eight assists in 132 appearances.
He also helped Sociedad claim silverware with a historic Copa del Rey Final win over Basque rivals Athletic Bilbao last year.
However, he will now focus on helping Newcastle finally land some silverware of their own after becoming the latest big-money signing added to Eddie Howe’s squad.
After the move was announced, Sociedad praised Isak for his ‘professionalism and dedication’ and confirmed some details of the deal agreed with the Magpies.
In a statement released on the official club website, they said: “Real Sociedad and Newcastle United FC have reached an agreement for the transfer of player Alexander Isak to the English team.
“The agreement includes a bonus for objectives and a percentage of a future sale.
“The Real Sociedad would like to thank Alex for the professionalism and dedication shown during his years of stay at our club, while wishing him all the best for his personal and professional future.
“Three seasons and scoring from the beginning in the fourth as Txuri Urdin, Isak has been one of the last great values of the Real Sociedad. Great protagonist in that historic cup qualifier against Real Madrid at the Santiago Bernabéu, Isak has won over the public for his dedication and determination in every action with our shirt.
“Forty-four times you have stood up your fans by jumping on your back. Thank you for everything, Alex.”
Isak could make his Magpies debut at Wolverhampton Wanderers on Sunday afternoon - if United receive international clearance ahead of the trip to Molineux.