Earlier this week Flood admitted he would have mixed feelings about leaving the Terrors.
And his affection for United was evident after signing for the league leaders.
He told the Celtic website: "I would like to thank Dundee United FC for all they have done for me.
"I have enjoyed my time there immensely and I wish the club all the best for the future.
"My focus is now Celtic and I can't wait to get started with my new club."
Celtic manager Gordon Strachan, who watched Flood shine for United in January's 2-2 draw at Celtic Park but miss a penalty in the Co-operative Insurance Cup shoot-out on Wednesday, said: "We are delighted to welcome Willo to Celtic.
"He has had a tremendous time at Dundee United where he has shown great ability, drive and enthusiasm. We look forward to working with him."
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