Rory McIlroy edged Tiger Woods to win the Honda Classic, becoming the No. 1-ranked player in the world in the process. (Mike Ehrmann/GETTY IMAGES)

Rory McIlroy won the most recent event on the PGA Tour, staving off a version of vintage Tiger Woods in the final round of the Honda Classic. He arrives here for this week’s WGC-Cadillac Championship newly minted as the No. 1 player in the world. In a month, he will pursue his second major championship at the Masters as a favorite, and in June, he will defend the U.S. Open title he won a year earlier at Congressional Country Club in Bethesda. He is, at 22, indisputably one of golf’s needle-movers, an exclusive club.

But when the PGA Tour returns to Washington for the first time in three years this summer, McIlroy won’t be there. He said Tuesday at Doral Golf Resort that even though he joined the PGA Tour this year and will play more golf stateside than he has in the past, he instead will play the Irish Open from June 28 to July 1 — the same dates as the AT&T National.

“Of course it was difficult,” McIlroy said of his decision. “You always want to go back to places where you’ve had success before. Obviously, I have great memories from Congressional last year.”

In part because of his historic eight-shot victory at Congressional last year, McIlroy is at a stage in his career which few golfers reach. His presence can help determine whether an event’s field is assessed as strong or weak. The AT&T National has traditionally had a tough time drawing the top European players — and an elite field in general — largely because of its place on the calendar.

Since Woods brought AT&T as a title sponsor and essentially saved PGA Tour golf in Washington in 2007, the tournament has been held on or around the July 4 weekend. But that is just two weeks, and one tournament, after the U.S. Open. The British Open is three weeks afterward, and by July, most top Europeans have already headed back home.

This year, the schedule is doubly prohibitive for McIlroy. The Irish Open has a strong pull for him because it will be played at Royal Portrush, just more than 60 miles north of McIlroy’s home town of Holywood, Northern Ireland. Some of McIlroy’s early reputation was built on the legendary course, which staged the 1951 British Open. He shot 61 there as a teenage amateur, and the Irish Open will be held there for the first time in 65 years. The event hasn’t been held in Northern Ireland at all since 1953.

“Having the Irish Open being played in Portrush, in my home country — to be honest, it was a tough decision to make,” McIlroy said. “But I’ll have plenty of chances to play Congressional again, and play the AT&T. The Irish Open may only be in Portrush for a couple of years.”

The AT&T National itself is making a return to Congressional after a two-year absence that allowed the club first to overhaul the greens on its signature Blue Course, then host the U.S. Open. The tournament was held at Aronimink Golf Club in suburban Philadelphia in 2010 and ’11, which received rave reviews for its Donald Ross-designed course.

Still, tournament officials are looking forward to returning to Washington — where Woods, whose foundation benefits from the event, hasn’t played since winning his own event in 2009. Woods missed the 2011 U.S. Open with injuries to his left knee and Achilles’ tendon.

Greg McLaughlin, the tournament director and CEO of the Tiger Woods Foundation, said in an e-mail Tuesday that he was getting “fantastic feedback” from players about the return to Congressional and the event itself.

Still, this year’s event won’t hold the possibility of another duel between Woods and the new world No. 1. It was Woods who closed the Honda Classic with a sterling 62 that provided McIlroy with a number for which to shoot — a number he beat, further solidifying himself as one of his sport’s elite draws.

“I can’t sit here and lie and say it didn’t feel better to have Tiger post a score and to be able to play solid,” McIlroy said. “It made it feel a little sweeter than had it been someone else.”