The winger joins Rovers for an undisclosed fee, believed to be in the region of £1million, and has signed a four-year contract at Ewood Park after undergoing a medical and agreeing personal terms on Tuesday.
Salford-born Marshall started his career at Manchester United as a schoolboy before moving on to Crewe, where he worked under Rovers' assistant manager Terry McPhillips and played in the same youth team as defender Grant Hanley.
At 17 he signed a professional deal with Stoke, enjoying several loan spells over a two-and-a-half-year period at Northampton, Cheltenham, Carlisle and Sheffield Wednesday.
Impressive displays during his time at Hillsborough prompted Leicester to make a move for Marshall in January 2012. He ended the season strongly for the Foxes with 18 appearances and four goals.
The England Under-21 international made 61 appearances for Leicester, scoring nine goals.
He is the third player to leave the King Power Stadium this summer following the exits of Jermaine Beckford and Richie Wellens as the Midlands club aim to fall in line with the Financial Fair Play regulations.