Gould will make about $5 million on the tag in the 2019 season after averaging $2 million over his first two seasons with the 49ers.
Gould originally joined the 49ers as a free-agent signing March 10, 2017. The Chicago Bears, who recently parted ways with kicker Cody Parkey, released Gould prior to the 2016 season.
The 36-year-old Gould spent 11 seasons with the Bears and became the franchise's all-time scoring leader. In his two seasons with the 49ers, he has converted 72-of-75 field goal attempts. He led the NFL in field goal percentage (97.1) in 2018.
In his 14 seasons in the league, Gould has made 358-of-408 field goal attempts (87.7 percent). His 87.7 career mark ranks second in NFL history among kickers with 100-or-more field goals made.