The Dolphins will also receive a 2018 seventh-round pick and send a 2018 seventh-round pick to San Francisco. The trade is contingent on Kilgore passing his physical.
Pouncey had requested to be released earlier on Thursday.
Kilgore re-signed with the 49ers earlier this offseason on a three-year contract. The 49ers signed center Weston Richburg in free agency this week. He will likely replace Kilgore at the position for the 49ers.
Pouncey, 28, was signed through the 2020 season as part of a five-year extension he signed with the team in 2015. With his release, the Dolphins save $7 million on their salary cap.
Pouncey told the Palm Beach Post on Thursday that he wanted a raise, but the request was declined.
"I gave this city everything I had," Pouncey told the Post. "I'm heartbroken."
"At the end of the day I'm a Miami Dolphin for life," Pouncey told the Post. "This city gave me an opportunity to play in the NFL. I think it was awesome. I had a hell of a ride here."
Kilgore, 30, was a 2011 fifth-round pick by the Niners. He emerged as a locker room leader and one of the team's most dependable veterans over the past couple of seasons.
"On behalf of the entire organization I want to thank Dan for everything he contributed to this team and the Bay Area community over the last seven seasons," 49ers general manager John Lynch said in a statement.
In 2017, Pouncey played his first 16-game season since 2012. He was coming off back-to-back seasons of major hip surgery but didn't show any effects of the injuries last season.
He is a three-time Pro Bowl selection, earning the honors in three consecutive seasons from 2013 to 2015. He has played in 93 games (all starts) since the Dolphins made him the 15th pick in the 2011 draft.
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.
ESPN's Nick Wagoner contributed to this report.