McIlroy held off a determined challenge from Sergio Garcia to lift the Claret Jug on Sunday at Royal Liverpool and claim his third major title.
The Holywood man is now placed behind world number one Australian Adam Scott.
McIlroy has been world number one on four occasions and a total of 39 weeks, losing it to Tiger Woods in March 2013.
Sergio Garcia's share of second in the Open with American Rickie Fowler has taken the Spaniard from ninth to fifth and helped ensure there are no American players in the top five. Fowler moved up from 25th to 18th.
Masters champion Bubba Watson is the highest ranked American in sixth, with Woods dropping from seventh to ninth after finishing 69th at Hoylake, his worst 72-hole finish in a major as a professional.
Among those who have passed on congratulations to McIlroy include Prime Minister David Cameron and former US President Bill Clinton.
Fellow Northern Irish golfers Darren Clarke and Graeme McDowell have also offered their congratulations to the young star.
However, G-Mac doesn't think McIlroy's success will lead to a return to the dominance of the game by one individual - as in the days when Tiger Woods regularly out-shone his competitors.
"For every Rory, there's an Adam Scott and Jordan Spieth and Sergio Garcia and a Tiger and a Phil (Mickelson)," McDowell said.
"There's too many good players now. It's so deep. It's so strong. Everyone is so good.
"I don't think we're going to see that dominance again for a while unless somebody comes out who has perfected the imperfectable."
McDowell wasn't taking anything away from McIlroy though.
"You can't play much better than Rory is hitting the ball. That's as good as it gets," the Portrush man added.
"Unfortunately you can't hole every putt, or else you'd be shooting 58 every day. It's just not happening."
Phil Mickelson, who McIlroy succeeded as Open champion, seemed to agree with McDowell's assessment.
"We used to say there will never be another Nicklaus, and then along came Tiger. You never want to discount the possibility of someone coming along and dominating," he said.
"But nobody has really asserted themselves week in and week out the way Tiger did for such a long period of time.
"We'll have great performances, like Rory this week. Like (Martin) Kaymer at the US Open and so forth. But it's very hard to do that week in and week out the way Tiger did. That's why it was so impressive what he did."