The Sweden international has signed a long-term contract at Saint James'Park to become Eddie Howe's fourth summer signing.
The Magpies, who have made a positive start to the season, have also added Matt Targett, Sven Botman and goalkeeper Nick Pope to their ranks.
Isak scored 44 goals in 132 games for Real Sociedad after joining from Borussia Dortmund in the summer of 2019.
He helped them win the Copa del Rey in his first season at the club.
'I'm delighted to have it done. It was a big, big decision for me but it is a decision I am really happy with,' Isak said after completing his transfer.
'It is a great, historical club that I think anyone would like to play for, with amazing fans. They were a big part of why I came here - and also the club's project, which is one that I really believe in.
'You always want to go into a team and know how they play. I think Newcastle play very attractive football and I want to be a part of that.'
Newcastle boss Howe added: 'I'm very excited that Alexander has chosen to join us. He is an outstanding talent who is capable of making a big contribution to the team.
'He is technically very good, with a mix of attributes that will complement us, but he is also at a great age to grow with this club.
'I want to thank the club's owners and transfer committee for bringing Alexander to Newcastle. We are all delighted to have him on board.'
The 22-year-old has been handed the number 14 jersey and could make his debut against Wolverhampton Wanderers this weekend.
