LONDON—Comcast Corp. and 21st Century Fox Inc. will settle their takeover battle for Sky PLC in a weekend auction run by British regulators, setting up a dramatic climax to a 21-month sale process that has pitted some of the world’s biggest media giants against each other.

The U.K. Takeover Panel, which polices deal making in the country, laid out rules for the auction on Thursday. It is a process the regulator hasn’t run many times previously—and never before with such a large company as the prize. London-listed Sky has a...