The 29-year-old won promotion in his first full season at the club and was attracting interest from fellow Championship rivals Derby earlier this summer.
However, Francis revealed his delight in committing his future to the Cherries until the summer of 2017.
"There was interest and a couple of bids from a club close to my home (Derby), but it never really came to much," he told the official club website.
"I'm just happy to have my future here sorted.
"To put it simply, this is the happiest I've been during my career.
"It's a great place to be and I'm very happy to have signed for another three years."
Francis first joined the Cherries on loan from Charlton in 2011, before making the switch permanent in the summer of 2012.
He featured in last week's season-opening 4-0 win at Huddersfield.