Anthony joins the Magpies after playing a starring role in Forest's impressive 2024/25 Premier League campaign, scoring six goals and adding 11 assists to secure European qualification.
The 23-year-old, a Swedish international team-mate of Alexander Isak, arrived at the City Ground in summer 2023 and has gone on to surpass 100 Premier League appearances.
Prior to making his move to the Midlands, Anthony came through the youth system at Manchester United, making his competitive debut and scoring his first Premier League goal in May 2021.
He has also established himself as a regular part of the Sweden squad, with four goals in 22 senior appearances after working his way through the international age groups. His most recent appearance for his country came in their 2-0 victory over Hungary last month, in which he played the full 90 minutes.
Newcastle United Head Coach, Eddie Howe, said: "I'm delighted to welcome Anthony to Newcastle United. He has been a key target for us so I'm delighted to secure him at this early part of pre-season.
"He is an exciting talent with attributes that make him a unique attacking threat. His pace, energy and ability to create and score goals will strengthen us and complement the way we want to play.
"Anthony is hungry to develop even further with us and to achieve success here, and we’re all looking forward to working with him."
Anthony said: "I'm excited, I'm really happy but most importantly I'm ready. I'm ready to put on this black and white top to really fight for this team and give everything for the passionate fanbase that lives and breathes football.
"I had an amazing two years at Nottingham Forest, they really helped me to become the player I am today, but I'm really happy to be here now. The club won a trophy last season and are building something unique, something special that I really want to be part of.
"I really want to buy into the culture, into the DNA of this club. I'm really happy to be here and I can't wait to get started."
Anthony's squad number will be determined during pre-season.