The Magpies have been in the market for a striker after Calum Wilson was ruled out of action for weeks.
Isak has now become Newcastle's fourth signing of the season following the arrival of Matt Targett, Nick Pope and Sven Botman.
The Swedish striker has expressed his delight after signing a long-term deal at St James' Park.
✍️ Newcastle United are delighted to announce the signing of Alexander Isak from Real Sociedad.— Newcastle United FC (@NUFC) August 26, 2022
Welcome, Alex! ??⚫️⚪️
"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.
"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 plays very attractive football and I want to be a part of that."
Newcastle United coach Eddie Howe also raved about the club's latest signing.
"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 scored 33 goals in 105 appearances for Real Sociedad in all competitions.
Isak has been handed the number 14, and he is in line to make his Premier League debut against Wolves on Sunday.