The architect exchanged vows with Suzanne Shaw in a romantic ceremony in The Hamptons, New York on St. Valentine's Day (14Feb12).
Cook admits he decided against going public with his wedding news over fears his nuptials would be brought up in his ongoing bitter custody battle with Brinkley.
He is quoted as telling the New York Post columnist Selim Algar, "I did not want to openly share this happy moment in our lives... (I worried) Christie would drag it into her black hole of revenge and hate like she does everything else good in my life."
Cook began dating Shaw after he split from Brinkley in 2008. Their divorce turned ugly when they began fighting for custody over their children, Jack and Sailor, and the division of their assets.
They're due to meet in court on Friday (22Jun12) for the latest hearing.