The two companies will front £92.6m (€130m) for the 167-bedroom property, each holding a 50% share, with Mandarin Oriental managing it under a long-term agreement.
They will then spend a further £64m (€90m) in renovating the hotel, adding a spa and new restaurant facilities.
The hotel first opened in 1910 and is located within an exclusive residential area close to Madrid’s financial and commercial district and a number of the city’s most famous cultural attractions, including the Prado Museum and Retiro Park.
It has several grand spaces that can be used to host events including the Salón Real, which can accommodate 400 guests, and the terrace and gardens with space for 600.
Edouard Ettedgui, group chief executive of Mandarin Oriental, said: "We are pleased to join with Olayan for this project, which presents an exciting opportunity to extend our portfolio to another key European capital city.
"This beautiful hotel will complement our award-winning property in Barcelona, and both should benefit from the overall economic recovery in the country," he added.
The Hotel Ritz Madrid reported gross assets of £392m (€129m) and an EBITDA of £1.8m (€2.6m) in the year ending December 2014. It is anticipated to have a positive impact on future Group earnings.
Mandarin Oriental Hotel Group currently has 20 hotels in Asia, nine in The Americas and 15 in Europe, Middle East and North Africa.
• For more features, as well as breaking news, sign up to C&IT Magazine's daily Newstracker here