The striker, who was playing in the Premier League on loan with Blackpool last term, has moved to the south coast from Derby for an undisclosed fee.
Despite a desperately small squad, Pompey had an outside chance of reaching the play-offs for much of last season and Varney expects them to be challenging again.
"I've experienced this league and know it'll be tough again," he said.
"Hopefully we can make Fratton Park a tough place to come and pick up a few points on the road as well.
"We've got a great blend with the lads who have signed and the experience that was here already. Hopefully we've got a chance of achieving good things this year."