The 25-year-old arrives from non-league Bromley on a two-year deal as a free agent - days after featuring in the FA Trophy final.
Dennis, who can operate wide or as a number 10, this season scored 13 National League goals and 22 overall as the Ravens finished ninth.
He also earned the Supporters' Player of the Season and was named in the Vanarama National League Team of the Season.
Dennis made eight appearances for Dagenham & Redbridge in League Two after emerging through the ranks, but dropped into non-league in February 2014.
Since then he has been instrumental for Bromley, culminating in starting Sunday's FA Trophy penalty defeat to Brackley Town.
He represents Pompey's second signing of the week, following Ronan Curtis' arrival from Derry City for an undisclosed fee.