Marshall had a controversial four-season stay in Denver, including a request for a trade last summer but capped with an NFL-record 21 receptions in a Dec. 13 game against Indianapolis.
He was selected for a second Pro Bowl appearance after the 2009 season and is the fifth player in NFL history to have three consecutive 100-catch years. Marshall caught 101 passes for 1,120 yards and 10 touchdowns last season.
He made 327 receptions for 4,019 yards and 25 touchdowns in 61 games for the Broncos.
The Miami Herald said the Dolphins will give up second-round picks in 2010 and 2011 in exchange for Marshall. ESPN reported the wide receiver agreed to a four-year contract with Miami that would pay him $47.5 million, with $24 million guaranteed. He also has one-year remaining on his agreement, which pays him $2.5 million, with Denver.