Pompey had hoped the 23-year-old goalkeeper would agree a new deal but instead on Tuesday Eastwood completed his switch to Championship Rovers, signing a two-year contract.
He wrote on his Twitter account: "Want to thank everyone at Portsmouth for my time there, especially the fans! Loved every minute.
"Delighted to be joining Blackburn Rovers."
Portsmouth last month signed John Sullivan from Charlton, who now looks set to be the club's number one next season.