Holders of more than 97 percent of Marriott shares and over 95 percent of Starwood shares voted in favour of the cash-and-stock deal, which was valued at $12.41 billion as of Thursday.
China's Anbang Insurance Group Co last week abandoned its $14 billion offer for Starwood Hotels, clearing the way for Marriott to buy the owner of Sheraton and Westin hotel brands.
Marriott raised the cash portion of its offer to $21 per share on March 21 from $2 per share, valuing the total bid at $73.42 per share as of Thursday.
Marriott said the deal was on track to close mid-2016.
"Our teams continue to plan the integration of our two companies," Marriott Chief Executive Arne Sorenson said.
The deal has cleared the pre-merger antitrust review in the United States and Canada and awaits approvals in the European Union and China.
By Ankit Ajmera and Arunima Banerjee