Briefly two shots ahead on the back nine in the final round at Pinehurst in June, McIlroy bogeyed three of the last four holes to finish a shot behind DeChambeau.
While McIlroy missed short putts on the 16th and 18th, DeChambeau conjured a brilliant par save from a bunker on the last hole.
McIlroy, who has not won a major since 2014, left the course moments later without congratulating DeChambeau or speaking to the media.
But five weeks on from the US Open, McIlroy crossed paths with DeChambeau for the first time as he arrived at Royal Troon for the 152nd British Open, which starts on Thursday.
"I said hello to him and we talked," DeChambeau said. "He said congrats so everything's great there.
"He's a fierce competitor. I know he's going to give the fans as much as he can this week. I'm going to be doing the same.
"We're going to be competing. Hopefully it will be another good battle."
After three weeks off, McIlroy returned to action with a tie for fourth place in last week's Scottish Open and has been keen to reframe what happened at Pinehurst in a positive light.
The world number two pointed out that, between 2015 and 2020, he had few genuine chances to win a fifth major, despite racking up numerous top 10s.
That changed in the 2022 British Open at St Andrews when he shared the 54-hole lead and covered his first 10 holes of round four in two under par before the birdies dried up and he was overhauled by Cameron Smith's 64.
In last year's US Open, McIlroy birdied the first hole during the final round at Los Angeles Country Club to briefly hold a share of the lead, but would not make another and ultimately finished one shot behind Wyndham Clark.
"I'd much rather have these close calls. It means that I'm getting closer," McIlroy said.
DeChambeau is the man in form, finishing joint sixth at the Masters and second at the PGA Championship before winning the US Open for his second major title.
The 30-year-old, who first won the US Open in 2020, had his best British Open finish two years ago when he came joint eighth.
"It all depends if I'm striking it well. I can come in here with the most confidence, obviously, off of a major championship win," he said.
"I know how to get the job done. It's just a matter of if I'm as consistent as I was at the US Open and a few other venues as well.
"If I can play the golf that I have been, I think I'll give myself a great chance."
