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.