The 27-year-old rejected an offer from Rangers after Celtic's Scottish Premier League rivals had a bid of about £500,000 accepted by County.
And Celtic will pay a similar fee after Commons passed a medical in Glasgow and accepted better personal terms.
He will be presented to the media by Celtic on Friday.
Celtic manager Neil Lennon told BBC Scotland on Wednesday evening: "He is a player on a list that we have been interested in for a while."
Mansfield-born Commons started his career with Stoke City and moved to Derby from Nottingham Forest in 2008.
Unfortunately, I think he has received an offer from elsewhere
Rangers assistant manager Ally McCoist
Commons' contract at Pride Park is due to expire at the end of the season and the winger capped seven times for Scotland had rejected a new deal with the Championship club.
That attracted the interest of both sides of the Old Firm.
And Rangers assistant manager Ally McCoist on Wednesday admitted defeat, believing that he had received a higher offer from another club.
"We made him an offer," he revealed. "Unfortunately, I think he has received an offer from elsewhere that is more financially beneficial to him."
Rangers manager Walter Smith insists the blow of missing out on Commons has not been compounded by the fact the winger has joined Celtic.
"It's just the fact we were in to try to get the player and we have not got him - that's the main thing," said Smith.
"Where he goes after that is really immaterial.
"He's not coming to Rangers and that's what we would have liked to happen."