NFL Network's Adam Schefter reports the deal is worth $36 million over six years, including $13 million guaranteed.
The Jaguars chose not to re-sign Terry Cousin, the team's nickel back the last three years, and safety Sammy Knight. Both 11-year veterans turn 33 before next season.
Florence could fill Cousin's role or replace cornerback Brian Williams, who would then move to safety.
Florence spent the past five seasons with San Diego, where he played 74 games and started 43 of them.
Florence, a second-round draft pick in 2003 who grew up in nearby Ocala, started the first 10 games last season before being replaced by All-Pro cornerback Antonio Cromartie.
Florence finished with a career-high 66 tackles, and had two interceptions, 10 passes defended and one fumble recovery.
He has nine career interceptions and 47 passes defended.
The Associated Press contributed to this report