The 6ft 4ins striker arrives from Real Sociedad and has signed a long-term deal at St. James' Park.
Isak becomes the Magpies' fourth first team signing of the summer after Matt Targett, Nick Pope and Sven Botman and will wear shirt number 14.
Alexander Isak said: "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 play very attractive football and I want to be a part of that."
Newcastle United head coach, Eddie Howe, said: "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."
Alexander Isak's career
At just 22 years old, Isak has strong experience at football's elite level, having played in the top divisions in Sweden, Germany, the Netherlands and Spain, as well as amassing 37 caps for Sweden, scoring on nine occasions for his country.
Born in Solna, Stockholm, and of Eritrean descent, he began his career at local club AIK before being snapped up by Borussia Dortmund.
Following a successful loan spell at Dutch side Willem II, during which he scored 13 goals in 16 Eredivisie appearances, Isak moved to Real Sociedad. He made an immediate impact in San Sebastián, scoring seven goals for the Blue and Whites in the 2019/20 Copa Del Rey as the club won its first major trophy since 1987.
In Isak's three full seasons at the Reale Arena, Imanol Alguacil's side achieved top six finishes in La Liga.