Deliveries of Boeing's new lightweight carbon-composite aircraft are scheduled for 2017 and 2018, the Los Angeles-based company said in a statement.
Air Lease Corp had already placed an order for four 787-9s in December last year, according to the Boeing website.
The company was founded in 2010 by Steven Udvar-Hazy, widely considered the pioneer of modern aircraft leasing.
Udvar-Hazy co-founded International Lease Finance Corp in 1973, later sold it to U.S. insurer AIG (AIG.N) and resigned to run his current company in February 2010.
Air Lease announced the 787 order shortly after it also emerged as a previously unidentified buyer for Boeing's latest model, a revamped medium-haul jet called the 737 MAX.
The deal is expected to involve 60 of the fuel-efficient jets and is worth some $6 billion at list prices. It is already included in a Boeing list of commitments that still must be converted to firm orders, according to the two sources who asked not to be named because negotiations remain confidential.
The MAX, which will feature new fuel-efficient engines when it comes to market in 2017, competes with the upcoming Airbus EAD.PA A320neo, which also will have new engines.
Neither Air Lease nor Boeing (BA.N) would comment on the 737 MAX order.
Air Lease also has a pending provisional order for 36 A320neo-family aircraft and plans to close an order for a further 16 in January 2013.
Industry experts believe Air Lease could announce the MAX order at the Farnborough Air Show in the UK in July.
The Wall Street Journal reported on Monday that Air Lease was close to a deal to finalize the 737 order.
Udvar-Hazy has criticized decisions, first by Airbus and then by Boeing, to upgrade their best-selling medium-haul jets with new engines rather than completely redesigning them.
A redesign would have generated greater fuel efficiency but taken longer to bring to market.
Boeing and its European competitor have notched up more than 2,500 firm and provisional orders between them for the revamped jets, which aim to provide 12-15 percent fuel savings.
Speaking at a conference last week, Udvar-Hazy conceded neither manufacturer was likely to build an all-new model in the crucial 100- to 200-seat market soon, and indicated the leasing companies would throw their weight behind the new models.
"For the time being, what we have is what we know," Udvar-Hazy told the AFCA air finance conference in Barcelona.
Udvar-Hazy said he saw most demand for aircraft at the higher end of the 100- to 200-seat category, corresponding to the 180-seat Airbus A321 and the Boeing 737 MAX 9.
"The large end of the narrowbody spectrum is where most sales will occur," he said, adding the average number of seats per airline departure was gradually rising.
Leasing companies tend to place orders where they think there will be most liquidity in the market.
However, analysts say many buyers will wait for further clarity on the design of the 737 MAX before completing orders.
So far, Airbus leads the race to sell the new fuel-efficient variants. It has won 1,289 firm orders and 266 provisional ones, including the 36 Air Lease A320neo jets waiting to be finalized.
Boeing, which considered a new plane but decided to catch up with Airbus by re-engining the 737 last summer, has sold 451 MAX aircraft. It has won provisional orders for 135 more from declared customers and over 400 that remain unidentified.
United Continental (UAL.N) is finalizing a deal with Boeing to buy at least $10 billion worth of revamped and current models after Airbus was bumped out of the race, industry sources say.
Continental, an all-Boeing airline which merged with United in 2010 to form the world's largest carrier, already operates the larger 737 models.
The founder of AirAsia (AIRA.KL), Tony Fernandes, meanwhile said on Twitter that the Malaysian low-cost carrier was set for further expansion this week, prompting speculation that it could buy conventional A320s to ensure its short-term expansion.
The airline placed a record order for 200 Airbus A320neo aircraft at the Paris Air Show last summer, but those enhanced jets will not enter service until 2015.
Reporting by Tim Hepher, Kyle Peterson, Karen Jacobs; Editing by Eric Meijer