Nick Walsh will be the fourth official at Ibrox on January 2, with assistants David McGeachie and Daniel McFarlane .
It is Madden’s sixth match between Rangers and Celtic, and his fourth league game involving the sides this season.
He was the man in the middle last month for Celtic’s 2-2 draw at Hibs and took charge of Rangers and Aberdeen on the opening day, plus a 5-1 Premiership win over Motherwell at Fir Park.
His last Old Firm appearance came in September last year with Odsonne Edouard and Jonny Hayes on target in a 2-0 home win at Celtic Park where Jordan Jones was also sent off.
Rangers have three games before the derby with St Johnstone, Hibs and St Mirren completing the 2020 calendar while Celtic face Ross County, Hamilton and Dundee United.
Bobby Madden’s next game is Dundee United v Motherwell on Boxing Day.