"We are very excited ... we have booked a venue," Burnham said. "We are getting married in Hawaii on January 12 of next year."
Luyendyk, 36, said the location, Maui's historic Haiku Mill, has an "old world feel" with "vines and greenery" and is "not your typical beach wedding."
The wedding will be private and not televised, unlike his romance with Burnham, he said. They are also planning to keep the guest list small, to about 100 people.
??'BACHELOR' EXCLUSIVE! ?? @BachelorABC couple @ariejr and @laurenburnham91 announce details about their upcoming wedding: They'll tie the knot at a private ceremony January 12 in Hawaii! https://t.co/f8u2wc159Spic.twitter.com/Hyd5cS8Iqv— The View (@TheView) May 23, 2018
"If we were able to get married tomorrow, we would," Burnham said. "We vibe well together, we're best friends. We're just ready for that next step."
The couple revealed that they have already bought a house in Scottsdale, Arizona, and have been traveling all over the world.Paul Hebert/ABCArie Luyendyk Jr. and Lauren B. on "The Bachelor." Read: Bachelor Arie Luyendyk Jr. explains why he filmed that shocking split Related: Becca Kufrin is the next Bachelorette
This is the second engagement for Luyendyk, who also proposed to Becca Kufrin at the end the regular season of the popular ABC reality-TV show. Luyendyk subsequently broke up with Kufrin to pursue a relationship with "Bachelor" runner-up Burnham.
During the "After the Final Rose" episode, Luyendyk popped the question to Burnham, who responded, "Definitely!"
On "The View," Luyendyk defended his actions.
"Because of how things ended, I think our relationship is stronger," he said. "I wouldn’t change it. We're happy"
Kufrin is now set to be the next "Bachelorette."
"I want to find love," Kufrin told host Chris Harrison on the "After the Final Rose" episode.
It appears she did. "View" co-host Sunny Hostin revealed that Kufrin has not only found love but is engaged
"The Bachelorette" premieres Monday at 8 p.m. ET on ABC.
ABC News' Allison Yang contributed to this report