FRHI Holdings owns three of the world's most famous hotel brands: Fairmont, Raffles and Swissôtel.
It has 155 hotels in 34 countries, with 42 in North America, including The Plaza in New York.
AccorHotels, which owns the Novotel and Ibis chains, said the purchase would give it a better-balanced profile.
The owners of FRHI include the Qatari Investment Authority and the Kingdom Holding Company of Saudi Arabia.
They will become major shareholders in Accor, with stakes of 10.5% and 5.8% respectively.
Accor will pay for the acquisition by issuing 46.7 million new shares, worth about €1.8bn based on Wednesday's closing price, and a cash payment of €786m.
The French company already owns luxury hotel brands including Sofitel and Pullman, as well as the mid-market Novotel and Mercure, as well as the budget Ibis and hotelF1 chains.
It said the deal would increase profits from the second year after the deal was completed, with €65m in revenue and cost savings expected.
Sebastien Bazin, chief executive of AccorHotels, said: "It offers us robust and global leadership in luxury hotels - a key segment in terms of geographic reach - growth potential and profitability, for long-term value creation."
"We are positioning ourselves as a key player in the current industry consolidation process while maintaining substantial leeway to implement our transformation plan."
The deal is the latest consolidation in the global hotel industry after Marriott International made a $12bn takeover of Starwood Hotels & Resorts to create the world's largest hotel operator.
FRHI was put up for sale earlier this year by its owners. It was reported in September that London-listed InterContinental Hotels Group was considering making a bid, but none materialised.
Sheikh Abdulla Bin Mohammed Bin Saud Al-Thani, chief executive of the Qatar Investment Authority, said it looked forward to becoming a significant shareholder in Accor.
The QIA will get two seats on the Accor board, while Kingdom Holding will have one.
The owner of hotels including the Savoy in London and Raffles in Singapore has been bought by Accor for €2.6bn (£1.9bn).