The 49ers confirmed the deal on Monday.
Dawson spent the past three years with the 49ers after kicking for the Cleveland Browns during his first 14 seasons in the NFL. He has connected on 86.2 percent of his kicks with San Francisco and was 24-of-27 in 2015, including a long of 54 yards.
Janie McCauley of the Associated Press shared insight on Dawson's decision to remain in the Bay Area.
"Dawson, who turned 41 in January, had said he wanted to play at least another season and expressed his desire to remain with the Niners despite no longer handling kickoff duties he so loves," McCauley wrote. "He enjoyed being a mentor to rookie punter Bradley Pinion last season."
Although Dawson kicked well last season—ranking 10th in accuracy—it's a smart move not to make a long-term commitment to a 41-year-old. Father Time can catch up with an athlete quickly, and if he does struggle, San Francisco can part ways without taking a significant salary-cap hit.