Olejnik has signed a three-year contract and joins Peterborough for an undisclosed fee.
“He has had a fantastic season with Torquay and is undoubtedly the best goalkeeper in that division,” Peterborough boss Darren Ferguson told his club’s official website.
“He has got good experience in Scotland, playing over 100 games (for Falkirk) and that is important.
“I have spoken to people in Scotland about him. We have had him watched on numerous occasions and we are happy to get him on board.
“There is still improvement in him. But he is willing to learn, has a good attitude and it is an important position to fill and we believe we have done very well to get him in.”