The 20-year-old, who has the option to extend his contract should he impress, spent the majority of last season with Skelmersdale United.
Tollitt told Pompey’s official website: “I’m made up. It’s my first professional contract and I can’t wait to get started.
“I can’t wait for the opportunity to step out in front of 17,000 people at Fratton Park.
“I want to be part of something with Pompey, to help them move up and go places. The club really shouldn’t be in this league.”