The order, the largest of the year by a major airline, calls for 25 of each plane with the option to buy 50 more of each, The Chicago Tribune reported.
United said it had plans to retire its fleet of Boeing 747 jumbo jets and Boeing 767s by the time the new planes are delivered.
For United, it is the first major order for new planes placed since the early 1990s, when the company ordered Boeing 777s and Airbus A320s.
Industry observers said with other airlines canceling orders for the long-delayed Dreamliner, the timing was right for United to place an order. With sales slow, the airline was likely to find discounts and other incentives, such as favorable financing terms, the newspaper said.
MarketWatch placed the value of the order at about $18 billion.