Speculation has surrounded the role at the struggling Championship side since Hill's departure last month, with O'Driscoll quickly installed as the favourite for the Oakwell vacancy.
A statement from O'Driscoll on the club's official website, following Thursday's board meeting said: "I'm very grateful to have had the opportunity to have spoken to Barnsley.
"In my one meeting with the directors I was keen to ascertain exactly what the short and long-term strategies and ambitions of the club are and how I may be able to help the club achieve those. At no point were terms discussed by either party.
"Barnsley is a well-run club whose achievements in successfully maintaining their Championship status for so many seasons should never be underestimated.
"The directors' commitment to and passion for Barnsley FC impressed me. But at this moment, and given the extremely disappointing and sudden nature of my departure from Nottingham Forest, I've respectfully declined the opportunity to become Barnsley's next manager.
"I wish the club, players and supporters all the best for the rest of the season."
Hill was dismissed by the Tykes after their home defeat to Blackburn, which saw the club sink to the bottom of the Championship.
Former Sheffield United boss Kevin Blackwell and ex-Sheffield Wednesday manager Gary Megson were also reported to be on the club's four-man shortlist.