Hibbert told BBC Radio Cambridgeshire: "Some big teams have come down, including ourselves, who I'm sure will be around the top of the league.
"But it should be a great season for us and we will be a match for anyone."
Hibbert, 24, joined Peterborough on a free transfer from Shrewsbury in May, signing a three-year deal at London Road.
The former Port Vale man scored 15 goals for the Shrews last season and will compete with Aaron McLean and Craig Mackail-Smith for a place in the Posh team.
Former Dagenham man Mackail-Smith hit 15 goals last season, while McLean found the net eight times.
"There's going to be a lot of competition for places and you've got to be up for a fight for your place," added Hibbert.
"Everyone's got a clean slate at the start of the season and it's important to hit the ground running."
Source: BBC Sport
Source: BBC Sport