The 28-year-old goalkeeper joined Pompey after his release from Torquay, who were relegated from the Football League last season.
He told the club's official website: "I only knew about the move last Friday. It was an easy decision for me to make and I'm looking forward to the new season.
"I'm not coming here to play second fiddle, but I understand that neither is Paul Jones.
"It's accepted at every club that there are two keepers challenging for a place in the side and I'm ready for the challenge."
Poke made 13 appearances for Torquay last season, including a 1-0 win for his side at Fratton Park - an experience which made up his mind long before Pompey showed interest.
"I came off at the end and said to my dad: 'Imagine playing in front of that crowd every home game.'
"There were about 15,000 people inside Fratton Park and although they didn't give the fans much to shout about that afternoon, it was still a special atmosphere.
"For a team like Torquay going there, it is obviously a rare experience to play in front of a crowd like that.
"It would be the same for almost every side in the division. It makes you want to go out and raise your game.
"It obviously didn't take long for me to think about coming to Portsmouth."