The Scottish international makes the move from Wales to Lancashire for an undisclosed fee, penning a two-and-a-half year deal.
Bowyer revealed that Conway has been on the Rovers radar for several months, so he is delighted to have finally secured his services.
"We are absolutely delighted," said the Rovers boss. "He is somebody that we had earmarked prior to him going on loan at Brighton this season.
"Then when he played against us he got a penalty and set the second one up with a quality cross, so we were even more impressed with him.
"He fits the bill of what we are always after which is good people first and foremost, and then obviously good footballers.
"He's an international, he knows quite a few of our lads so he'll settle in very quickly.
"He brings something a little bit different to the squad, especially now Marshall is now out for a while.
"The deal that we have done is a fantastic deal for the football club, we are looking forward to him playing for us."
The winger has been registered in time to feature in this weekend's fixture against Blackpool subject to international clearance.
Tickets for Saturday's match against are currently on open sale. Tickets are priced from £19 for Adults, £12 Seniors and £7 Juniors. Why not book online today and collect your tickets from the Blackburn End collection point on the day of the game.