The former Everton man has struggled to nail down a regular starting place at St James' Park since arriving as one of club's first signings on their return to the top flight in 2010.
Having been signed by Chris Hughton, he failed to stake a claim in the side under successor Alan Pardew and was loaned to Blackpool in October where he played 14 times, scoring twice.
Gosling, an England Under-21 international, will move to Dean Court on a four-year deal from July, subject to a medical, having been told his contract will not be renewed.
Bournemouth manager Eddie Howe explained the Championship club had to fight off plenty of competition but believes Gosling can help them improve on their 10th-place finish this season.
"He is a box-to-box central midfielder who has lots of energy. He is very good technically and also has a goal in him," he told The Bournemouth Echo.
"He is an attack-minded player who can do all disciplines of the game so I think he will complement our team very well.
"We are looking to build all the time and I think he will give us different options as well.
"We had to fight off some competition to get him and it is always a good sign when other clubs are interested.
"We are delighted he chose us ahead of them and I think he was attracted by our style of play and our vision for him so, hopefully, it is a good match and we will both get when we are looking for from the signing."
Having struggled with injury early in his time at Newcastle, Gosling made just 36 appearances during his four-year spell at the club.
