Brown, 29, rushed for 4,815 yards and 36 touchdowns and caught 184 passes for 1,491 yards in Miami. He ran for 1,000 yards in 2006 and made his only Pro Bowl team in 2008.
"Ronnie is an all-around running back with a versatile skill set," Eagles general manager Howie Roseman said in a statement released by the team. "He can run the ball, catch it, and does very well in pass protection. He'll add some good size to our backfield, and he's a good character guy. We think he'll be a tremendous compliment to LeSean (McCoy) and the other young backs on this team that we really like. You can never have enough good running backs in this league, and we are happy to have Ronnie join us."
Before adding Brown, the Eagles' only experienced running backs were starter McCoy, who ran for 1,080 yards and caught 70 passes last season, and Eldra Buckley, who has just 36 carries in two years with the team.
Right tackle is a question mark for the Eagles, with Winston Justice, the starter the past two years, beginning training camp on the injured list with a knee injury. The team has been using second-year pro Austin Howard and former seventh-round draft pick King Dunlap at right tackle during the early days of camp.
Harris started 16 games in 2008, eight in 2009 and 10 last season.
"I appreciate everything the Broncos have done for me," Harris told the Denver Post. "I'm grateful they drafted me, and I built a lot of great relationships with a lot of great people over the past four years. It wasn't an easy decision. But in the end, money had nothing to do with my decision. This was about what I thought was the best opportunity at this point in my career."
Like all other NFL free agents, Brown, Harris and Page aren't permitted to practice with their new team until Thursday.
The Associated Press contributed to this report.