There had been speculation that rival InterContinental Hotels Group had been plotting a raid on Starwood but it is Marriott that has made the move.
Together the two companies operate or franchise more than 5,500 hotels with 1.1 million rooms worldwide.
Starwood operates the Sheraton and Westin brands.
Arne Sorenson, president and chief executive of Marriott International, said: "The driving force behind this transaction is growth.
"This is an opportunity to create value by combining the distribution and strengths of Marriott and Starwood, enhancing our competitiveness in a quickly evolving marketplace.
"This greater scale should offer a wider choice of brands to consumers, improve economics to owners and franchisees, increase unit growth and enhance long-term value to shareholders."
Bruce Duncan, chairman of the board of directors of Starwood Hotels & Resorts Worldwide, said: "During our comprehensive review of strategic and financial alternatives, it was clear that our talented people, world-class brands, global leadership and spirit of innovation were much admired and key drivers of our value.
“Our board concluded that a combination with Marriott provides the greatest long-term value for our shareholders and the strongest and most certain path forward for our company."
