The Scottish international put pen-to-paper on a two-and-a-half year deal until the summer of 2016, joining from Cardiff City for an undisclosed fee.
"I'm just delighted to be here," said Conway. "I came here last night and met the manager and saw the facilities and I was really impressed, so I'm really happy to be here.
"I've spoke to Grant and Jordan a few times and asked them about the club and the manager and they had nothing but good things to say.
"My agent had spoke to Blackburn a few months ago and he had nothing but good things to say about the manager and liked his style.
"When I met him last night, he's a really nice guy and I got on really well with him, I just liked what he had to stay.
"Blackburn are a massive club, I've played at the stadium a few times, it is a great stadium with good support.
"So when I came here and saw the facilities it just sealed it."
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.