Pouncey is under contract through 2020 as part of a five-year extension he signed with the Dolphins in 2015.
Now the Dolphins will need to address the starting center position in either free agency or the Dolphins.
San Francisco will send Kilgore to South Florida with a seventh-round pick and receive a seventh-round pick in return, according to ESPN's Adam Schefter.
Kilgore was acquired in exchange for undisclosed compensation, the 49ers announced.
The Dolphins will accomodate Pouncey's request.
Although Pouncey played in all 16 games a year ago, the Dolphins had concerns with his injury history, which is probably the reason the team wanted him to take a pay cut.
"I think it was awesome", he said.
Kilgore, 30, was the 49ers' second-longest tenured player behind left tackle Joe Staley, and a month ago Kilgore re-signed (three years, $12 million) to stay off the free-agent market. "We are pleased to be able to help find Dan a great situation to be able to continue his career". With his release, the Dolphins save $7 million on their salary cap.
In 2017, he started a career-high 16 games at center for the 49ers and was named the victor of the team's Bobb McKittrick Award, which is given annually to the 49ers offensive lineman who best represents the courage, intensity and sacrifice displayed by the longtime offensive line coach, during his 21 years of service to the 49ers.
Pouncey, who was a team captain last season, also was one of the central figures in the locker room bullying scandal involving former Dolphins offensive lineman Jonathan Martin.
Pouncey was a first-round pick by the Dolphins in 2011. He joins Ndamukong Suh and Jarvis Landry as offseason departures from Miami. Previous year he completed the season but it was clear that his multiple hip surgeries had taken its toll and Pouncey lost some of his push upfield.