The Rolling Stone guitarist downed shots and vodka and cranberry juice with the actor at the star-studded opening of the luxury 950 million pounds Hotel Atlantis complex in Dubai this week.
"This is my great friend now, we're going to cause havoc," News of the World quoted Wood, as saying.
Wood, who has split from wife Jo, arrived a day late without his new 20-year-old Russian girlfriend Katia Ivanova.
"I've left Kat back in London. I missed the first night but I'm having a great time and there's a lot of making up to do now," he added.