The 26 year-old signed a three-year contract at Ewood Park after agreeing personal terms on Monday. The clubs had agreed a fee believed to be in the region of £2.5 million last week.
Szmodics joined Posh from Bristol City for around £1 million in August, 2020.
Szmodics made 96 appearances in all competitions for Posh including a successful loan stint, scoring 27 goals and played a big part in the club getting promoted to the Championship with 15 goals in the 2020-21 season. The former Colchester United man made his last Posh appearance on Saturday as Grant McCann’s men came from behind to beat Cheltenham Town 3-2.
Posh chairman Darragh MacAnthony said: “Sammie and his wonderful family will be missed. A true Posh legend who lit a fuse under us to get promoted back the Championship two years ago. He deserves this move and I will be a fan from afar.”