Dolan, 18, was released by North End recently after his second year as a scholar.
Speaking last week, PNE manager Alex Neil name-checked Dolan when saying some of the youngsters who had been released could count themselves 'very unfortunate'.
On Wednesday morning, Dolan posted a thank-you message to North End on Twitter.
In it, he thanked staff and team-mates for their support from start to finish, with him saying it had made him a 'better player on the pitch but also a better person off the pitch'.
Rovers announced his signing on Wednesday lunchtime.
Speaking to their official club website, Dolan said: "It’s a dream come true to sign my first professional deal at a club as big as Blackburn Rovers.
"The hard work continues, so I just can’t wait to get my feet going again, hit the ground running and show everyone what I can do.
"For me, my preferred position is as a number 10, but I can play on the wings as well. I’m a direct player, with confidence, and I just like to get the ball, express myself, enjoy my football and show everyone what I can do.
“This break has made me even more eager to get going again with football. I talk to my dad about setting visions and goals, and here at Rovers I’ve got the highest expectations.
"The history of the club is amazing, with some great players coming through the system, and I’m willing to work hard to be one of those players."
Dolan is the third scholar released by North End to find a new club, defender Tyler Williams having signed for Stalybridge Celtic and striker Louis Potts for Workington.