The transaction includes the assumption of debt and a contingent cash consideration of up to $50m to Prestige shareholders, which would be payable upon reaching certain performance metrics for 2015.
Norwegian will finance the acquisition with existing cash and debt facilities, and the issuance of around 20.3 million shares of its common stock.
Norwegian Cruise Line CEO Kevin Sheehan said: "The acquisition of Prestige represents an extraordinary opportunity for Norwegian Cruise Line to expand our market presence by adding two established, award-winning brands in the upscale cruise segment with loyal followings.
"Not only does this acquisition immediately enhance our financial performance, but it also deepens the bench of talent that we have been developing over the years."
Norwegian Cruise operates cruise liners such as Norwegian Sky and Norwegian Spirit and recorded a revenue of $2.57bn in 2013.
Prestige chairman and CEO Frank Del Rio said: "The combination is very compelling and will allow us to further enhance our renowned guest experience.
"We are looking forward to joining the Norwegian team and building upon the success that our three brands have already achieved."
The transaction is expected to close in the fourth quarter of this year and is subject to regulatory approvals and customary closing conditions.