The 22-year-old, who began his career at Fulham before spells at MK Dons, Dundee United, Oldham and Yeovil, has left The Hive to sign a two-year deal with Rovers.
Marsh-Brown joined Barnet in 2013 and struggled to break into the first team last season as the club were promoted to the Football League from the Vanarama Conference.
He made two league starts in 11 appearances for the Bees and scored two goals.
A statement on Barnet’s official website said: “Barnet FC can confirm that Keanu Marsh-Brown has left the club in order to sign for Forest Green Rovers on a two-year deal for an undisclosed fee.
“Everybody at Barnet FC would like to thank Keanu for all of his efforts with the club and we wish him well in the future.”