The 21-year-old has signed a three-year contract and completed the paperwork at the idverde Training Ground on Wednesday (June 22) lunchtime.
It is believed that he had a release clause in his Orient contract that Posh have now paid.
Kyprianou is a Cypriot Under-21 international and has come through the youth academy at the London club after leaving Spurs as a 14-year-old. He has spent three loan spells in non league but appeared 38 times time in League Two last season for the O’s. In total, he made 80 appearances for the club.
He spent most of last season playing in the centre of a midfield three ans has been described as a holding midfielder.
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Posh boss Grant McCann said: “It is great news that we have managed to get Hector. He is a very good physical presence, a ball-winning midfielder and very good on recoveries. He passes forward and likes to break lines with passes and forward runs.
“He can play as a 6 or as an 8 and he can also play in a back three if we needed, his versatility is a real plus for us. We are really looking forward to working with Hector to help him improve and progress.”
Kyprianou added: “I am really happy to be here. I felt like it was the perfect club for me and I can’t wait to get started. I really enjoyed my time at Leyton Orient, but when I heard about the interest from Peterborough
United, it was something that really appealed to me. They are a club that give young players an opportunity, but they are also very ambitious, they want to get promoted from this division.
“I can play in a few different positions within midfield and pre-season is about knuckling down and trying to show what I can do in training and in the games that we have coming up. I have already done a few days training with Orient so I am looking forward to getting started here.”
Kyprianou will wear the number 22 shirt.