The 28-year-old, who has four England caps, made 187 appearances for the Cherries and scored 67 goals.
Wilson is Steve Bruce's third summer signing since the collapse of the proposed takeover of the club in July.
"From the minute I knew Newcastle were interested, it was definitely something that appealed to me," Wilson told the club's website.
"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."
The Newcastle manager said: "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."