The 21-year-old forward joins the Lancashire club for an undisclosed fee and has agreed a four-year contract at Ewood Park.
Marshall joined the Foxes from Stoke City in January 2012 and made 61 appearances in all competitions for Nigel Pearson's side, scoring on nine occasions. He most recently featured as a late substitute in the 3-2 win at Nottingham Forest on the final day of the 2012/13 league season.
The Club would like to thank Ben for his efforts during his time in a Leicester City shirt and wish him well in his future career.