Ryanair: "Going to be a monster"
The deal is one of Boeing's biggest contracts so far this year, helping to make up for a 45% drop in new orders in 2001 as airlines cut costs in the wake of the 11 September attacks.
While the Ryanair order carries a face value of $9.1bn, Boeing is believed to have offered substantial discounts.
Ryanair said that the aerospace giant's offer was "exceptionally competitive."
The airline expects to take delivery of the new aircraft between 2002 and 2010.
News of the order comes two weeks after Ryanair rival Easyjet asked Boeing and Airbus for a quote on 75 planes.
Ryanair's monstrous ambitions
Ryanair, Europe's biggest budget airline, last year reported hefty profits and steady passenger numbers, shrugging off the global slowdown and the impact of 11 September.
The carrier said its expanded fleet will help to turn it into Europe's largest airline in terms of passenger numbers by 2010.
"Ryanair is going to be a monster in Europe in the next 10 years," Ryanair chief Michael O'Leary said.
Boeing's largest single order last year was a contract to supply 22 aircraft to China Southern Airlines.
Also on Thursday, Boeing sold a US-based plant which makes components for F22 fighter aircraft to UK engineering group GKN for $4.8m.
In the City, Ryanair shares stood 5p lower at 387.5p in lunchtime trade.
Easyjet order
Easyjet, which has also managed to dodge the slump in passenger numbers, also has major expansion plans.
The firm aims to carry more passengers than all but the biggest three European airlines - BA, Air France, and Lufthansa - by 2008.
Ryanair and Easyjet, which fly exclusively on short-haul European routes, are seen as less prone to terrorist attacks than long-haul national carriers.