The deal runs through the 2025 season and includes $6.5 million fully guaranteed, per Schefter.
Bailey, 25, was entering the final year of his rookie contract, and carried a salary-cap charge of $4.05 million -- the second highest of any punter in the NFL.
"I'm just so happy and blessed I get a few more years here," Bailey said after Monday's practice, adding that it is a "huge milestone" in his life.
"Any time there is uncertainty, it's always something in the back of your head. But at our position, you have to be able to compartmentalize and execute, and if you're not able to do that with whatever is distracting you, you're not going to play very long."
The extension is expected to lower his cap charge by about $1.85 million, increasing the Patriots' overall cap space to about $4.75 million.
While the team gains cap relief, the 6-foot-2, 205-pound Bailey -- who entered the NFL as a fifth-round draft choice out of Stanford -- earns some long-term security.
He punted 49 times last season and posted a 47.3-yard average (eighth in the NFL) and 39.6 net (21st in the NFL). He also handles kickoff and holding duties.
Bailey's powerful leg is especially helpful to the Patriots when weather conditions turn colder and windier later in the season in New England. Coach Bill Belichick places a notable emphasis on winning the field-position battle, and Bailey has often been effective in helping the team do so.
In 2020, when he was named first-team All-Pro, Bailey punted for a 48.7 average and 45.6 net, with just five touchbacks.