Long-serving Bob Symns stepped down last year leading to the £100k per year role (£150k with bonuses) to be advertised.
Paton previously worked as an interim consultant with Blackpool FC. He never formally held a role at the club, although he did work as a consultant while the club was in receivership following the 2019 court case, which saw the Oystons ousted.
Paton was used until the club was sold to current owner Simon Sadler in July 2019.
Paton started work at Posh earlier this month, although the club have not yet formally announced his appointment.