McCain, a fifth-round draft pick by the Dolphins in 2015, had 46 tackles and an interception in 2020. In his six seasons with the team, he had 7 interceptions, 4 sacks and a forced fumble.
He is scheduled to visit the Washington Football Team on a free agent visit Monday, a source told ESPN's Adam Schefter.
McCain, who was due a $6.4 million non-guaranteed salary this season, started 55 of 87 games for the Dolphins. After the transaction, Miami would create $5.6 million in cap space and have roughly $1.5 million in dead money.
He had signed a four-year, $27 million extension with the Dolphins in June 2018.
McCourty, 33, has 137 career starts, including 11 last season for the Patriots. He will be reunited Flores, a former Patriots assistant. The chance to play for Flores again was a driving factor in McCourty's decision, a source told ESPN's Mike Reiss.
McCourty has also played for Tennessee and Cleveland.
Tight end Jibri Blount, who played basketball at North Carolina Central and was the Mid-Eastern Athletic Conference player of the year in 2019-20, was also signed and took McCain's roster spot.
The Associated Press contributed to this report.