The striker has arrived from Ipswich for and undisclosed fee – believed to be around £450,000 – and signed a three-year deal.
Harrison endured a difficult campaign at the Tractor Boys last term.
He netted just once in 17 appearances as the Portman Road side were relegated from the Championship.
Blues boss Kenny Jackett has been a long-term admirer of the 25-year-old, though.
And having scored 14 times during his final season at Bristol Rovers, Harrison feels he can again hit the goal trail at Fratton Park.
He said: ‘I’m buzzing to get it done – it’s been a long time coming. I can’t wait to get going now.
‘I’ve played at Fratton Park a couple of times and, to say the least, it’s not quiet on a Saturday or a Tuesday. It is very loud!
‘It was tough last season for me, obviously. But now it is about bouncing back next season.
‘I’m coming down with an open mind and need to get my confidence back.
‘I have always loved football and I have always had confidence, but now it’s about showing everyone else that I can do it.’