The bride and the "Drink to That All Night" singer exchanged vows at sunset overlooking the Atlantic Ocean from atop the historic Spanish fort Castillo de San Cristóbal, a rep confirms to PEOPLE exclusively.
"I'm looking forward to seeing what the world has in store for us as a married couple," Niemann, 35, tells PEOPLE.
The couple, who requested their 100 wedding guests donate to charity in lieu of giving wedding gifts, got engaged last October in New Orleans – though things didn't go as smoothly as Niemann had hoped. His romantic plan to propose during a horse-and-carriage ride was given a reality check by Petek, 33.
"We were walking over to Jackson Square, and we turn the corner and see, like, 13 carriages just waiting for someone to rent them," the country singer told PEOPLE at the time. "So I'm like, 'Hey, you want to take a ride?' She's like, 'Nah. Horses are supposed to be in pastures, not walking the streets of New Orleans!' I just thought, 'Oh, crap!' I was literally frantic."
But the quick-thinking Niemann improvised. "We walked over to this statue in Jackson Square, and I just turned to these ladies and said, 'Would you be kind enough to take our picture? I think we might be getting engaged,' " said Niemann. "Morgan was like, 'What?' Then I took out the ring. Morgan was crying; the ladies were crying ... It was a cool moment."