Gould, 35, played 10 games for the New York Giants last season. He converted all 10 of his field-goal attempts and was 20-of-23 on extra points.
A fixture with the Chicago Bears for 11 seasons, Gould has made at least 80 percent of his field goals in 10 of his 12 NFL campaigns. He was a Pro Bowler and first-team All-Pro in 2006 but largely settled into a role of being a steady, reliable hand from nearly any range.
The Penn State alum has never missed a field goal inside 30 yards and has missed only 11 from inside 40. Phil Dawson handled kicking duties in San Francisco for the last four seasons, but Dawson signed with the Arizona Cardinals earlier Thursday, per ESPN's Adam Schefter.
The 49ers have been busy in the early part of free agency, coming to terms with seven free agents (including Gould). They have been highlighted by a contingent of players with whom new coach Kyle Shanahan, most notably wide receiver Pierre Garcon.