Woods drawn with McDowell, Oosthuizen
Second-ranked Rory McIlroy has been grouped with American left-hander Phil Mickelson, last week's Scottish Open winner, and Japan's Hideki Matsuyama.
Woods, who will be making his first competitive appearance since last month's US Open, played nine holes in practice on Sunday.
The 14-times major winner said he still needed medication and treatment on his injured left elbow.
He had been suffering with minor discomfort ahead of the US Open at Merion where he aggravated the problem and was seen wincing and shaking his arm on several occasions.
“I started chipping and putting a little over a week ago and I'm full go for the British Open,” the 37-year-old American said on his website on Saturday.
“I'm very confident my elbow strain won't be a problem and I will be able to hit all the shots I need to hit.
“The big thing at Muirfield will be to avoid the rough,” added Woods. “Although I have been playing every day I also have to get back into a competitive feel.”
Woods is making his second appearance at a Muirfield-hosted British Open after finishing tied 28th in 2002. “My first visit didn't go very well. I caught the worst of the weather,” he said. “That's just the nature of links golf. Luck plays a big part in it and you never know what you're going to get.”
World number seven McDowell is one of golf's hottest players this year, having won the World Match Play Championship in Bulgaria, the RBC Heritage in South Carolina and this month's French Open in Versailles.