Kardashian, 42, posted a carousel of photos from the momentous occasion on Instagram Wednesday, including shots of the pair kissing and embracing, as well as candid snaps of them on the beach.
"I woke up all night thinking it was a dream," the Poosh founder wrote.
Responding to her post, Barker, 45, replied, "Forever with you is a dream come true."
The Blink-182 drummer shared similar photos on his own Instagram page, captioning the post: "My fiancé."
"My favorite person in the world," Kardashian replied to Barker's post. "My fiancé."
"I worked on it with Travis and he was a really big part of it," Schwartz told PEOPLE. "He was really hands-on in the whole making of it. It's gorgeous and they're happy."
The engagement came as a "complete surprise" for Kardashian, a family friend told PEOPLE.
"Travis told her family that he planned to propose, but everyone was great at keeping it secret. The Rosewood is their favorite for short weekend getaways. They often stay at the hotel," the source said. "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."
According to the insider, Kardashian "can't wait to marry" Barker and she "would also love to have a baby with him."
Getty Travis Barker and Kourtney Kardashian
Kardashian and Barker have been dating for nearly one year. When PEOPLE confirmed their relationship in January, a source said "they've been friends for a long time but it's turned romantic."
Barker shares son Landon, 18, and Alabama, 15, with ex-wife Shanna Moakler, who he was married to from 2004 to 2008. He has also remained close with Moakler's 22-year-old daughter Atiana, whom the 46-year-old model shares with boxer Oscar De La Hoya.
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Kardashian shares sons Mason, 11, and Reign, 6, and daughter Penelope, 9, with ex Scott Disick. The pair split in 2015 after dating on and off for nine years.
A source told PEOPLE that Disick, 38, is "not happy" with Kardashian and Barker's engagement.
"Scott never approved of Kourtney dating Travis. He has struggled with their relationship," the insider said. "He always had this idea that he and Kourtney would eventually get back together. He was pretty shocked when he found out that she was dating Travis."