The deal, which sees Japan's biggest carrier switch from Rolls-Royce engines to ones supplied by General Electric, is a boost for Boeing after it posted no January orders for the first time in decades.
ANA's order includes 11 787-10 stretch versions and four shorter 787-9s. It also has options for a further five 787-9s. The first delivery will be in the business year beginning April 2022, the airline said in a news release on Tuesday.
In a separate filing, ANA said 12 of the 15 aircraft on firm order would be purchased directly from Boeing and the remaining three from a subsidiary of Japanese trading house Sojitz Corp, with which Boeing has longstanding commercial ties.
ANA was the launch customer for the 787 programme and is the world's biggest operator of the planes. The new additions would bring its purchase total to 98, of which 71 are in service.
It operates all three models of the plane, the 787-8, 787-9 and 787-10.
The order is a blow to Rolls-Royce, which has supplied all of ANA's 787 engines so far. Problems with the engines which required extra inspections led the Japanese carrier to cancel hundreds of flights in 2018.
In London, shares in the British engineering firm fell as much as 1.8%, underperforming a slightly weaker market.
"As the 787 becomes a larger share of our fleet size, we have made the decision to diversify some of the components to minimize single source risks," an ANA spokeswoman said.
Air New Zealand Ltd, a Rolls-Royce customer for its initial 787 fleet, last year ordered GE engines for its latest order of eight planes, meaning it will also operate both types in the future.
(Reporting by Eric M. Johnson in Seattle and Tim Kelly in Tokyo; Additional reporting by Jamie Freed in Sydney; Editing by Himani Sarkar, Edwina Gibbs and Jan Harvey)
By Eric M. Johnson and Tim Kelly