Wilson has signed a four-year deal with an option to a fifth-year on Tyneside, if he chooses.
Villa withdrew their offer after hearing through Wilson's agent that the player wanted to join Newcastle over the second city club.
Wilson has made 126 Premier League appearances, scoring 41 goals and assisting a further 16.
The former Coventry City striker has four England caps, scoring his only goal for The Three Lions against the USA.
Wilson spent six years on the south coast, with his best season in a Bournemouth shirt coming in the 2018/19 season - where he scored 14 league goals and assisted 10.
The England international becomes Newcastle’s third most expensive signing of all-time - behind Miguel Almiron who joined for £21 million and Joelinton who arrived for a club-record £40 million last summer.
Wilson has arrived in time to feature in Newcastle's season opener against West Ham on Saturday.
Wilson: ‘It’s a massive club with great history’
Wilson said: “From the minute I knew that Newcastle were interested, it was definitely something that appealed to me.
"It's a massive club with great history. Along the years, they've had great strikers so if I can emulate half of what they've done, I'd like to attempt that.
"I believe in my ability as a player. As a striker I think it's important to set yourself goals long term and short term, and I'm hoping to achieve them.
"With the players around me, I believe we can get the goals we need as a team and I want to help contribute to that."
Bruce: ‘I’m delighted to get him’
Head coach Steve Bruce added: "Callum is somebody I’ve admired for a long time and I’m delighted to get him.
"He has done fantastically well at Bournemouth and was deservedly playing centre forward for England less than two years ago.
"The club has worked ever so hard to get Callum here and we have beaten off competition from a number of clubs.
"I’m grateful the club has made it happen. Lee Charnley and those behind the scenes deserve a lot of credit."