The forward has moved to the Blues from Ipswich Town for an undisclosed fee – believed to be around £450,000 – and signed a three-year deal.
Boss Kenny Jackett has been a long-term admirer of Harrison, having tried to sign him in the past two transfer windows.
The 25-year-old arrives to bolster Pompey’s forward options ahead of their renewed push for the Championship next season.
And Gallen feels the ex-Bristol Rovers man has the attributes to take the Blues into the second tier.
The assistant manager said: ‘We’re really pleased to get Ellis here – he’s someone we’ve kept tabs on for around 18 months now.
‘We’ve always liked him as a player. He can fit into our system as a number nine and hold the ball up, win headers and scores goals.
‘He also brings added mobility to that position and has the right attitude, which is really important for us and fits into our philosophy.
‘Ellis has a good record in League One and all the attributes we need. We feel he has the whole package and can add to our squad.
‘With the players that we’re starting to bring in, we’re confident that they can make the difference for us in getting out of this league.’