The 38-year-old kicker missed 13 of his 42 field-goal attempts during the 2012 season.
General manager Trent Baalke said in a statement: "The 49ers would like to thank David for his service, dedication and leadership over the past two years.
"He is a true professional who represented himself and this organisation with class. We wish him, and his family, all the best."
Akers tied the record for the longest ever field goal in the NFL in 2012, making a 63-yard effort against the Green Bay Packers.