O'Neil, 25, was unsettled on Teesside in the second half of last season following his £5million summer switch from Portsmouth.
However the two men have discussed the matter and Southgate received the news which he had been hoping for.
The manager said: "I am delighted. He has come back a lot more settled and he is determined to try to give it a go.
"He feels after the second half of last season, he owes us a little bit, and it is fantastic to know that.
"I am delighted. He was superb up to Christmas for us and then because he was unsettled and doing a lot of travelling, that affected his performances.
"But I am thrilled that he has come back and wants to play a big part with us because we know the quality of his play."