The 20-year-old made 32 appearances in the Championship in the 2018-19 season as City narrowly missed out on the play-offs.
"It's a fantastic club. The move has come around quite quickly, but I'm happy to be here and can't wait to start playing," he told Bournemouth’s official website.
"Premier League football is what I've always wanted to achieve. I want to play as many games as possible and I feel like this is the right place for me to try and do that."
Bournemouth boss Eddie Howe is pleased to have added another young talent to his squad, following on from the arrivals of Dominic Solanke, Chris Mepham and David Brooks over the past year.
"Lloyd is an exciting talent and a player of real potential, while at the same time already possessing good experience for someone so young," Howe said.
"He is athletic, versatile, physically excellent and has a very bright future ahead of him.
"I’m delighted that we have been able to strike so early in the summer and look forward to working with Lloyd during the coming seasons."
The club's chief executive, Neill Blake, added: "I’m delighted to complete the transfer of Lloyd.
"Over the last few years we have secured some of the brightest homegrown, young players in the game and believe we have done so again with Lloyd.
"There was interest in him from a number of other clubs so it was important to make a move early, and under the tutelage of Eddie Howe I believe Lloyd will be an excellent addition to the squad."
Kelly, who has earned three caps for Aidy Boothroyd's England Under-21 side, will compete with the likes of Charlie Daniels and Diego Rico for the left-back position at the Vitality Stadium.
Bournemouth ended the 2018-19 Premier League campaign in 14th place in the table, with a 5-3 final-day defeat to Crystal Palace allowing Newcastle to jump ahead of them in the standings.