An approach from Championship side Barnsley was turned down earlier in the week, but a bid from the Blades was accepted on Wednesday evening.
The striker is now due in Yorkshire on Thursday, with the move having to be completed within 24 hours to beat the transfer deadline - after midnight no Football League clubs will be able to sign players until January.
"Colin made it clear to me he no longer wished to play for Brighton; as a result we have reluctantly accepted the bid from Sheffield United," said Brighton boss Mark McGhee..
"I am really disappointed and I feel personally let down by Colin. We gave him the chance to get out of Bury and I don't think he's repaid us for that, we felt Colin could have built his career here at Brighton.''
Brighton have had a £150,000 bid for Barnet striker Tresor Kandal rejected by the Bees, and will not be making an improved offer.