Hume was left out of the matchday squad when the two sides met at the Stadium of Light on Saturday, with Lee Johnson saying it would have been unfair to involve him given the expected move this week.
Johnson had confirmed earlier in the week that Hume, who stalled on the offer of a new contract for much of the summer, was frustrated with his lack of game time since returning from injury.
Talks accelerated rapidly since then and Hume has now put pen to paper on a two-and-a-half year deal at Fratton Park, with the club holding the option of automatically extending for another year.
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"Denver is a young player who wants to get better every day and he brings us some outstanding athleticism and energy," Cowley said.
“He will add quality in the final third and we really like his wonderful ability to receive the ball on the back foot and play forwards.
“We’re a forward-thinking team and the attributes he possesses are really aligned with our way of playing.
“It’s great that he can play as a left wing-back or on the left of a back four because it gives us the flexibility we want in our squad.
“He has all the attributes in his toolkit to be a really good defender and we’re looking forward to working with him.
“Everyone we contacted spoke so well of Denver in terms of his professionalism and the way he conducts himself," Cowley added.
“He was a breath of fresh air from the moment we started talking with him and you can see his ambition. He also loves football and for us, that’s really important.
“I’m really excited about the business we’ve done this January and I believe we’ve made some real progress.”
The 23-year-old departs Sunderland having made 84 competitive appearances for the club, scoring three goals and adding ten assists.
His departure leaves Dennis Cirkin and Niall Huggins as the club’s recognised left backs, though Huggins remains sidelined with a stress fracture of the back.
Sporting Director Kristjaan Speakman said the move was a ‘natural progression’ for the defender, who is eager to play on a more regular basis.
“Naturally, Denver wants to be playing regular football to move his career forward, but he’s found himself out of the team and played less than 20 games in the past 12 months,” Speakman said.
"As an academy graduate, we want to support and maximise his development and this is a natural progression for him in the current circumstances.
"We look forward to watching Denver’s future development from afar and we wish him the best of luck at Fratton Park.”
The club statement added: “All at SAFC echo Kristjaan’s well wishes and thank Denver for his contribution over the last 13 years.”
Hume could make his debut against Charlton Athletic at Fratton Park on Monday night.