The 24-year-old joined Rovers on transfer deadline day signing a four-year deal at Ewood Park.
A number of clubs had been linked with Dann throughout the summer, but Blackburn won the race for his services.
Dann, who worked under Kean at Coventry, is relishing linking up again with the Scot at Blackburn.
"It's happened quite late but I'm glad to get it done and get started really," Dann told the club's official website.
"When you're involved in it it's not the best thing to be involved in, so I'm just glad to get it done.
"I've worked with the manager before and know what he's about and that was a big factor for me, and with the new owners (Venky's) it's a good time to come to the club."