The 28-year-old joins for an undisclosed fee, putting pen-to-paper on a two-and-a-half year deal to the summer of 2016.
Conway started his footballing career at Ayr United, before moving to Dundee United in 2006.
The midfielder would go on to make 166 appearances during a five-year spell at Tannadice, scoring on 16 occasions.
Fine form for Dundee United saw him gain international honours for Scotland - to date Conway has seven caps to his name.
June 2011 saw the wideman make the move south to Cardiff City, playing a key role as the Bluebirds gained promotion to the Premier League last season.
This season he enjoyed a three-month spell on loan with fellow Championship club Brighton & Hove Albion, winning the penalty in the Seagull's 3-0 victory over Rovers at the beginning of November.
Conway links up with fellow Scotland team-mates Grant Hanley and Jordan Rhodes, as well as former Cardiff frontman Rudy Gestede here at Ewood Park.
The winger has been registered in time to feature in this weekend's fixture against Blackpool subject to international clearance.