The Sunday proposal at the Rosewood Miramar in Montecito, California was filmed for her family's upcoming Hulu show, a source tells PEOPLE.
"Since this is Kourtney's first engagement, it's of course a big deal," the source says. "Most of her family was there to celebrate. Two of Travis' kids were there too. They enjoyed a private, family dinner at the hotel."
"It was a beautiful celebration," adds the source. "Everyone is very happy for them. Her family loves Travis."
A rep for Hulu did not immediately respond to PEOPLE's request for comment.
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The Kardashian/Jenner family announced in December 2020 that they had signed a multi-year deal to "create global content" that will stream exclusively on Hulu in the United States and in multiple international territories on Star beginning in late 2021.
The news came two months after they announced the end of their long-running E! show Keeping Up with the Kardashians, which had been documenting their lives since 2007. KUWTK concluded after 20 seasons this June.
During the Disney Upfronts in May, Kris Jenner called the switch to the Disney-owned streaming platform a "no brainer."
"This is the next chapter," said Jenner, 65. "In the new show, you'll see us evolving as a family. Fans want us to be who we are and since moment one, they've been emotionally invested in our show, just like we are. The fans will love seeing us continue the journey. I can't say much about what's coming, but spoiler, we're going to look fabulous and everyone's going to watch."
Barker, 45, proposed to Kardashian, 42, on the beach in the middle of a massive heart-shaped floral arrangement surrounded by candles. "Forever," Kardashian captioned photos of the special moment.
Alabama Luella Barker Instagram Kourtney Kardashian and Travis Barker
"It was a complete surprise for Kourtney. Travis told her family that he planned to propose, but everyone was great at keeping it secret," a separate source revealed to PEOPLE. "The Rosewood is their favorite for short weekend getaways. They often stay at the hotel. This is why Travis proposed there. It's a very special place to them, but it was also easier to keep everything a secret by proposing there."
"Kourtney is of course ecstatic," the source added. "She can't wait to marry Travis. She would also love to have a baby with him."
Jeff Kravitz/Getty Travis Barker and Kourtney Kardashian
Kardashian shares three children — Mason, 11, Penelope, 9, and Reign, 6 — with ex Scott Disick, 38. Barker was previously married to Melissa Kennedy from 2001 to 2002 and Shanna Moakler, 46, from 2004 to 2008. He shares stepdaughter Atiana, 22, son Landon, 17, and daughter Alabama, 15, with Moakler.