Newcastle have signed the Sweden international from Nottingham Forest for a fee of £55m.
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."
Elanga also said: "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."