The Republic of Ireland international has signed a four-year deal at Ewood Park after agreeing personal terms.
Rovers agreed a £2.5 million fee with The Lions last week for the highly-rated midfielder and have been locked in talks with the player.
Pompey entered the race for Reid's signature last week and had hoped to hold talks with the player over a move to Fratton Park.
The move ends a long hunt for Rovers boss Graeme Souness, who has been chasing Reid for several months now and he will help bolster the midfield after the departures of Damien Duff, David Dunn and Keith Gillespie.
Souness was delighted to have landed Reid and revealed he wants to make more signings before the start of the new season.
"We've signed Steven Reid tonight and I think both Brett and Lorenzo are good signings for us - I feel we will be stronger than this time last year," said Souness.
"It's a four-year deal. I raced over here because discussions went on quite late but my understanding is he has signed now. I'm delighted to have him on board.
"We've had five players leave the club and I think we've replaced four so we've got a bit to go and we've not spent any of that money yet - this is money we set aside.
"We are going to try and be cautious. I've got confidence in the squad and I'm not going to rush out and spend money."
