Cook, 60, asked Alba Jancou, 21, to marry him while in Santorini, Greece last month and she said yes.
Cook told People that they are “very happy.”
“We consider ourselves incredibly lucky to have found, in each other, our soulmate,” the architect told Page Six. “We are looking forward to many years of wedded bliss!”
Cook, who shares his 24-year-old son Jack and 21-year-old daughter Sailor with Brinkley, has reportedly been in a relationship with Jancou for about a year.
Cook took to Instagram to celebrate National Daughters Day and posted a photo of Sailor from Dancing With The Stars.
“Happy belated national daughters day! I’m proud of the courage and skill my daughter has demonstrated on dancing with the stars! XOXO,” Cook wrote.
This will be Cook’s third marriage. He was married to model Brinkley, 65, from 1996 to 2008. Cook was then remarried to Suzanne Shaw, 38, and the pair split in 2014.Follow @KatieScottNews