The Northern Irishman is trying to win a green jacket to complete a career grand slam.
Northern Ireland's McIlroy, trying to win a green jacket to complete a career grand slam, and Spaniard Rahm, fresh off a runner-up finish at the World Golf Championships Match Play in Austin, Texas, will join Japan's Hideto Tanihara on the first tee at 1:41pm (1741 GMT) Thursday in the third-to-last group on the famed 7,435-yard layout.
"I've played with a few of the Asian contenders, so I sort of expected one of those guys," McIlroy said. "And then Jon Rahm, I haven't played with him competitively. We played 18 holes, a practice round, in Austin. I'm really impressed with his game."
World number one Dustin Johnson will tee off in Thursday's final trio alongside fellow Americans Bubba Watson, a two-time Masters champion, and Jimmy Walker, who won his first major at last year's PGA Championship.
The field of 94 also features some morning groups sure to excite Thursday spectators, notably the 10:34 am trio of 2015 Masters and US Open winner Jordan Spieth, two-time major winner Martin Kaymer of Germany and England's Matthew Fitzpatrick.
The group behind them includes five-time major winner Phil Mickelson, trying to become the oldest Masters champion two months shy of his 47th birthday. The US left-hander will be joined by South Korea's Kim Si-Woo and Spain's Rafael Cabrera-Bello.
Just behind them, in what will be the final group to begin play in Friday's second round, will be Australia's third-ranked Jason Day, England's Justin Rose and American Brandt Snedeker.
Defending Masters champion Danny Willett of England tees off Thursday at 12:35 pm alongside US Amateur champion Curtis Luck of Australia and American Matt Kuchar.
Europeans once dominated the Masters, winning six times in seven tries from 1988 to 1994, and could surge again this year with a record 11 Englishmen in the field of 94, McIlroy on solid form and Rahm, 22, having won his first US PGA title at Torrey Pines earlier this year.
"He's a great young player," McIlroy said. "He'll be a huge asset to our European Ryder Cup team in years to come. I'm looking forward to it."
Rahm will have plenty of pressure as he approaches his first Masters tee shot.
"I'll be very excited on the first tee," Rahm said. "I know the first tee shot I'm going to be really, really pumped up, so I don't know how it's going to go.
"I want that, 'Oh my God, I'm playing in the Masters' moment, to be as short as possible. I know it's going to happen. It might take one hole or two holes but I want it to go away as soon as possible. I don't want to get to my 12th hole and be like, 'OK, we're 3-over par, let's get to work.'"