Lawrence, who came through the Manchester United’s youth academy, joined Leicester on a four-year deal last summer but failed to nail down a first-team place.
Lawrence told the Rovers website: “It’s a good club and I can’t wait to get going now. I knew there was interest but it has all happened so quickly, I’m just happy that is all done”.
Lawrence struggled to make an impression at the King Power Stadium last season and was subsequently sent out to Rotherham on loan, scoring one goal in six games.
He returned to make four brief appearances for the Foxes as they successfully staved off relegation in the Premier League.
Lawrence made his Manchester United first team debut in Ryan Giggs’ last game in temporary charge at the back end of the 2013/14 season in a 3-1 win over Hull.
The forward has also represented Wales at U21 level and will meet up with some familiar faces at Ewood Park.
“I know a few of the lads here already so I’m sure I’ll get a bit of stick. I was with Shane Duffy at Yeovil and I know Adam Henley from my time with Wales so it is good,” he said.
Lawrence goes straight into the squad for this weekend’s game against Brighton, provided his registration goes through in time.