The forward has signed a three-year deal at Fratton Park after arriving from Ipswich for an undisclosed fee – believed to be around £450,000.
Blues boss Kenny Jackett has had Harrison on his radar for a significant period of time.
He was keen to bring the 25-year-old to Pompey last summer when he was at Bristol Rovers before he moved to Ipswich.
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But after just one season at Portman Road, Harrison has departed for the Blues.