The 50 new aircraft will be delivered between 2025 and 2028, or around the same time that Norwegian's aircraft leasing deals come to an end, and the contract includes an option for 30 more, the company said in a statement.
The order is welcome news for the US manufacturer's flagship Boeing 737 MAX 8, which was grounded for 20 months following two fatal accidents and has been gradually returning to service since late 2020.
Norwegian and Boeing have meanwhile been locked in a legal battle for several years, with the Norwegian carrier launching legal proceedings against the US giant for compensation following setbacks related to its 737 MAX and 787 Dreamliner long-range jets.
The low-cost airline did not say Monday whether the order was part of any dispute resolution.
Norwegian said the deal remains subject to "various closing conditions" that it hopes will be concluded by the end of June.
Norwegian, which currently operates 61 aircraft, plans to ramp operations to have 70 in service this summer and 85 in the summer of 2023.
Plagued by over-ambitious expansion, technical problems and the Covid pandemic, the company narrowly avoided bankruptcy last year via an extensive restructuring that led it, among other things, to give up its long-haul flight, reduce its fleet and cancel numerous orders.
For Boeing, this order solidifies the revival of the 737 MAX, of which the British carrier IAG -- parent company of British Airways -- has also just ordered 50 examples with an option for 100 more.