After completing his move to Tyneside, the 26 year old Scotland international told Newcastle's official website: "It's an unbelievable feeling to come to a football club like this.
"I loved it at Bournemouth - I had a fantastic time there and it had a huge impact on my career. But when a club like Newcastle comes calling, I couldn't pass up this opportunity.
"It's fantastic to be here and I'm really looking forward to the challenge of getting the Club back in the Premier League."
Toon Boss Rafa Benitez added: "We have been following some wingers for a while and Matt was one of the best prospects for this team.
"He has great ability and pace, and as soon as we knew that Andros Townsend could be leaving, our priority was to finalise this deal.
"We have signed an exciting winger who has experience in the Championship but has also proved that he can step up to the top level. I am delighted that he is now part of our squad."