Marquis has joined the League Two club on an initial month's loan with a view to extending it until January.
The highly-rated 21-year-old has yet to feature this season for Millwall and he is keen to go out on loan to get some regular first-team football.
Pompey boss Guy Whittingham is thought to have beaten off interest from a number of League One clubs to land Marquis, who scored Millwall's winner against Aston Villa last season.
Marquis is relishing the chance to link up with Pompey and is hoping he can boost their promotion bid during his time at Fratton Park.
"I am really looking forward to going on loan to Portsmouth and I hope I can get some games there and score some goals," Marquis told Sky Sports.
"It is all about playing games for me and currently I am not playing at Millwall so it was important for me to go out on loan.
"There are a lot of strikers at Millwall and there is a new manager so this is a chance for me to go to Portsmouth and prove my worth.
"There was quite a bit of interest but I decided to go to Portsmouth and I cannot wait to get started."
Marquis believes the loan spell can only benefit him and Millwall by working under former striker Whittingham and playing on a regular basis.
"The manager was a proven striker during his playing career and if I can pick up a few things from him in training that can only be good for me," added Marquis.
"Portsmouth are a big club and their fans are among some of the best in the country so I am really looking forward to playing in front of them at Fratton Park and I promise to do my best for them for however long I am there."