The 60-year-old architect has asked Tulane University student Alba Jancou to be his wife, and the 21-year-old has accepted.
Sources tell Page Six Cook popped the question back on 15 September in Santorini, Greece.
"We consider ourselves incredibly lucky to have found, in each other, our soulmate," he says. "We are looking forward to many years of wedded bliss!"
The couple, which started dating last year (18), is planning a destination wedding in Europe.
Jancou is the same age as Cook's model daughter, Sailor Brinkley Cook, who recently competed on "Dancing with the Stars".
He split from his daughter's mother in 2006 when he was caught having an affair with an 18-year-old office clerk.