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In a conversation with PEOPLE, Ryan Wolfe, the lead pastor at Grace Christian Center of Las Vegas, says the couple had "their own vows that they wanted to share with one another" during the surprise ceremony held at A Little White Wedding Chapel on Saturday night.
While Wolfe was circumspect about the actual vows, he says "they had their own words and they were beautiful words to each other."
"It was an emotional moment they shared with one another," he adds. "You can definitely see the love that they have for each other."
After a busy night hosting five 9 p.m. weddings, Wolfe says he and his fellow A Little White Wedding Chapel employee, wedding coordinator Kenosha Booth Portis, were starting to close up when Lopez, 52, and Affleck, 49, pulled up in an SUV.
On The JLO Ben Affleck and Jennifer Lopez
"We were locking up everything, and they get out and we were like, 'Okay, well I guess we can do one more,'" Wolfe recalls. "So they walked in, and I know Jennifer Lopez, of course. But you don't expect to see Ben Affleck and Jennifer Lopez walking through the door every day."
As Lopez and Affleck — wearing a white dress (possibly the "dress from an old movie" she posted a video of herself wearing in her On the JLo newsletter sharing news of the wedding) and jeans and a white T-shirt, respectively — sat in the lobby of the chapel, Wolfe says he thought, "They look very familiar."
"I didn't recognize them [at first]," he says. "I think it was just because I didn't expect to see them."
Shortly after their arrival, Wolfe walked the two stars to areas where they could change into their wedding best: an elaborate, off-the-shoulder lace design by Lebanese designer Zuhair Murad for the bride and a white tuxedo jacket, black slacks and a bow tie for the groom.
"Jennifer was going to go change in our break room, and then as I was walking Ben Affleck to the restroom outside the men's public restroom, he said, 'No, I don't need anything fancy. I'm not fancy,'" Wolfe says. "I walked him out there, and then all of a sudden it just hit me. I'm like, 'That's Ben Affleck! That's Ben Affleck!' You don't want to make them feel uncomfortable so you don't want to get so nervous and so starstruck, but it was hard not to do."
For the ceremony, Wolfe says Lopez and Affleck "wanted just a regular wedding."
"She walked down the aisle to the regular 'Here Comes the Bride' processional, and she had flowers and he had a boutonnière on," Wolfe says.
After they recited their vows, Wolfe says he "was able to bless them and pray over them very quick, literally like an eight-second prayer."
Then, "they exchanged rings," Wolfe says. "It was a beautiful wedding."
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On The JLo Jennifer Lopez and Ben Affleck
Beyond Wolfe and Booth Portis, there were only two other people in attendance at the ceremony: Lopez's 14-year-old daughter, Emme, and one of Affleck's three children. (Lopez shares twins Max and Emme with her ex-husband, singer Marc Anthony; Affleck has Violet, 16, Seraphina, 13, and Samuel, 10, with ex-wife Jennifer Garner.)
"One of his kids were there and one of her kids, and they were the witnesses," Wolfe says. "Now they have to be 18 to be the legal witness, but I allowed their kids to sign their souvenir document. So they signed that and I gave that to them. And then of course our coordinator, Kenosha, had to be their official witness on the official license."
Throughout the ceremony, Wolfe says the kids seemed "thrilled."
"At the end of the ceremony, they were almost giddy excited, jumping around," he says. "You could tell [the two kids] also were close, had a good relationship, really liked each other. They were very excited and you could tell they really were happy."
The kids also helped with the wedding photography.
"Their kids took pictures during the wedding, and then I set up Ben's phone there in the chapel and they videoed the ceremony," Wolfe says. "There was no professional photographer."
By the time the ceremony was over, Wolfe says it was "close" to or "after midnight."
"I won't say it was a long ceremony, but it was more lengthy than what our normal ceremonies at the chapel are," he says. "And then, of course, they took tons of pictures after in [Elvis Presley's] pink Cadillac and in the chapel, but just with their phones. They were very thrilled with the ceremony, and they complimented and loved everything about it."
On The JLO
In her On the JLo newsletter, Lopez said the ceremony was indeed "exactly what we wanted."
"When love is real, the only thing that matters in marriage is one another and the promise we make to love, care, understand, be patient, loving and good to one another. We had that. And so much more," she wrote. "Best night of our lives."
Lopez, who rekindled her romance with Affleck last year and announced their engagement this past April, added, "Stick around long enough and maybe you'll find the best moment of your life in a drive-thru in Las Vegas at 12:30 a.m. in the morning in the tunnel of love drive through, with your kids and the one you'll spend forever with. Love is a great thing, maybe the best of things — and worth waiting for."
Based on his experience with the couple, Wolfe believes Affleck and Lopez are "soulmates."
"I 100 percent believe that they will last," he says. "They will make it. I really do believe they're meant for each other."