6:45 AM PT -- Jesse Grice, Reverend Elvis who officiated, tells TMZ he was booked for the wedding a week ago but wasn't told who was getting hitched. We're told Joe and Sophie booked the entire Chapel from 8 PM to 12 AM ... so no other weddings were going down. Grice says he recognized the Jonas Bros, but had no idea who Sophie Turner was because he doesn't watch "Game of Thrones."

Grice serenaded Joe and Sophie to "Viva Las Vegas" after the "I dos."

BTW ... Joe and Sophie got married on what would have been the 52nd anniversary of the marriage between Elvis and Priscilla.

7:40 AM PT -- After the wedding, the night was just getting started. Joe and Sophie found their way back to their hotel, where they jumped in the Jacuzzi wearing their wedding duds.

Guess what happened last night? Joe Jonas and Sophie Turner got hitched, and their wedding could not have been more different than the Nick/Priyanka nuptials.

Here's the way it went down ... the Jonas Bros performed at the Billboard Music Awards Wednesday night in Vegas, and afterwards they all beelined it for the Little White Wedding Chapel. Yup, Elvis is in the building.

You wouldn't know a wedding was going down by appearances, because Sophie didn't wear a wedding dress, although she looked super good in a white blouse and slacks.

So, there's inside the Chapel L'Amour, and the Elvis impersonator comes out and before long Joe and Sophie say to each other, "I promise you, I will never leave you. I will love and trust you all the days of my life, in sickness and in health, forever and ever."

Country stars Dan + Shay were there to sing Sophie down the aisle, and Joe's bros, Nick and Kevin, looked on as groomsmen ... and that was pretty much it.

They followed tradition and posed in front of the Cadillac at the Chapel and, of course, with the Reverend Elvis in red -- and they were husband and wife.

Oh, and this ... they exchanged ring pops as wedding bands!!!

Turns out they applied for a marriage license earlier in the day in Vegas. That doesn't necessarily mean the wedding wasn't planned -- they probably waited to make sure it all stayed secret.

A few celebs were on hand, including Diplo and Khalid ... the whole thing was super casual and pretty damn cool. BTW, Diplo captured the action inside the chapel on Instagram Live.

It COULD NOT have been more different from the endless wedding of Nick Jonas and Priyanka Chopra, which was beyond elaborate and lasted 9 years.

CONGRATS!!!!