Southgate said: "Gary is a player that I have always had a strong interest in since I first got the job here.
"Despite his relative youth, he has played 200 games for Portsmouth and he has captained their team.
"He's in the right age bracket and he has the hunger that we are looking for. He is a ready made Premier League player."
There were reported fears over O'Neil's fitness following a summer ankle operation, though scans which took place at the time of his medical showed nothing more that routine scar tissue.
Southgate said: "We are absolutely delighted with Gary's high level of fitness.
"He is fit, and he is exactly the kind of player who I hope will be forming the basis of the team here for the next few years and help push us up the table to where we want to be.
"A lot of people keep saying that we needed to strengthen the right side and Gary has certainly played there a lot for Portsmouth.
"We have now got competition for places all over the field and I'm absolutely delighted about that.
"In fact I am very happy with the business that we have done over the summer.