The Northern Irishman has been paired with Woods and Australian Robert Allenby for his first two rounds at Augusta and will tee off at 16:41 BST on Thursday.
The 31-year-old played with the American star in the third round of the Masters back in 2009, with Woods shooting 70 to McDowell's 73.
But much has changed for both players in the last two years, with Woods now slipping down the rankings and failing to win a tournament in 2010 and McDowell going in the opposite direction after winning the US Open at Pebble Beach last year.
The Portrush star has enjoyed an excellent start to the year on the PGA Tour and has secured three top 10 finishes already.
McDowell admits that he struggled to handle the pressure of playing with a 14-time major winner in years gone by but is no longer fazed by his presence on the tee.
"I feel like I've played with him enough now to where it's pretty normal once you get used to the whole buzz that surrounds him, especially inside the ropes," he said. "I've got to go and play my own game and let him play his game.
"I would have been intimidated a couple of years ago, but nowadays it's reasonably normal. I was expecting to get a draw somewhere along those lines this week."