The 20-year-old made 32 appearances in the Championship in the 2018/2019 season as City narrowly missed out on the play-offs.
A left-sided defender, Kelly, who was linked with Liverpool, Arsenal and Southampton, has agreed a long-term contract to join the Cherries.
"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 said.
"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, coming after 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."