The striker headed Kenny Jackett’s wish list last summer, with the Blues willing to pay big for the player who scored 25 goals in 30 appearances for Cheltenham during the 2017-18 season.
Pompey were unsuccessful in their bid to lure him to Fratton Park, though, with the front man opting to sign for Championship Bristol City for a £1.5m fee.
Yet he failed to hit the heights expected of him at Ashton Gate, with the 24-year-old starting only once for the Robins and appearing six times in total. He also failed to score for Lee Johnson side.
Yet there seemed to be plenty of interest in the striker from elsewhere.
Eisa confirmed he chose Posh over several other clubs, after moving for an undisclosed fee that is believed to be a Peterborough transfer record.
The London Road side spent £1.25m on striker Britt Assombalonga from Watford in July, 2013.
Eisa said: ‘Peterborough wanted me the most. They showed the most interest in me and showed how serious they were to get the deal done.
‘I met the chairman and the manager and they have showed nothing but love for me and that is what I need.
‘I know all about the strikers that have scored goals for Peterborough in the past and hopefully I can do that here.
‘I want to score goals, but I am not selfish, it is about the team and the team’s objective is to get to the Championship and I want to help the team in that goal. I am looking forward to getting started.’
Eisa represents Peterborough’s sixth signing of the summer, with former Pompey left-back Dan Butler among those to make the move to Posh.