The trio will tee-off at 14:45 local time on Thursday and at 09:44 on Friday.
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 in Pennsylvania, 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 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 Open appearance at Muirfield. His first attempt at the East Lothian course back in 2002 saw him finish tied for 28th, with his chances ruined when he ended up playing through that week's very worst weather during the first two rounds.
"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.
Oosthuizen won The Open, golf's oldest Major, at St Andrews in 2010.
Defending champion rnie Els, US Open winner Justin Rose and American Brandt Snedeker feature in another marquee three-ball at 09:11 in Thursday's opening round at Muirfield.
Masters champion Adam Scott has been drawn to play with American Matt Kuchar and Britain's Luke Donald at 14:12.
Lee Westwood and Sergio Garcia play alongside former Masters champion Charl Schwartzel of South Africa, while the fans will be squinting into the distance if they choose to follow the big-hitting group of Belgian Nicolas Colsaerts and US Ryder Cup duo Dustin Johnson and Bubba Watson.
Selected first round tee-off times (BST)
Bubba Watson, Nicolas Colsaerts, Dustin Johnson (8:44)
Nick Faldo, Tom Watson, and Fred Couples (09:00)
Justin Rose, Ernie Els, Brandt Snedeker (09:11)
Ian Poulter, Keegan Bradley, Billy Horschel (09:22)
Rory McIlroy, Hideki Matsuyama, Phil Mickelson (09:44)
Lee Westwood, Charl Schwartzel, Sergio Garcia (14:01)
Adam Scott, Matt Kuchar, Luke Donald (14:12)
Rickie Fowler, Matteo Manassero, Hunter Mahan (14:23)
Tiger Woods, Graeme McDowell, Louis Oosthuizen (14:45)
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- Rory McIlroy
- Tiger Woods