The Singapore-based company, owned by the Bank of China, said the bulk of the orders was for 50 B737 MAX 8 planes and 30 next-generation B737-800s.
The 80 planes have a value of $8.14 billion based on 2014 catalogue prices published on Boeing's website.
The orders will allow BOC Aviation to build on its fleet for the next seven years, the company said in a statement.
The firm said it has also ordered two B777-300ER aircraft, worth a total $660 million at catalogue prices. Both planes have already been placed with an existing customer, it added.
US aircraft maker Boeing said in a separate statement that the order is the "largest in BOC Aviation's 20-year history" and is part of the leasing firm's effort "to grow its portfolio of fuel-efficient airplanes".
Robert Martin, BOC Aviation's managing director and chief executive, said the fresh B737 orders followed a similar purchase made in 2006 for 50 B737 next-generation aircraft.
"This is a continuation of our commitment to be responsive to airline customers which are expanding or replacing older fleets," he said.
"The 737 is known for its operational and fuel efficiency, and BOC Aviation expects healthy demand for the next generation 737 and 737 MAX in the next seven years."
As of June 30, BOC Aviation said its fleet of 251 delivered aircraft included 118 Boeing aircraft operated by 27 airlines.
At the Farnborough airshow in July, BOC Aviation also ordered 43 Airbus single-aisle A320 passenger jets worth $4.4 billion at list prices.
Boeing has projected a travel boom in the Asia Pacific region over the next 20 years from 2013, fuelled by a rising middle class and strong regional economic growth.
"As income levels rise, Asia Pacific is set to become the largest air travel market in the world. In 2033, approximately 48 percent of global traffic will be to, from, or within the region," Boeing said in its latest regional forecast.