The couple, who first met early last summer, secretly became engaged four months ago on a romantic trip to India.
David, 35, proposed to Jodie on the shores of Lake Pichola in magical Udaipur, Rajasthan, and was overjoyed when the model and TV presenter instantly said 'yes'.
They immediately told both their families, including Jodie's parents and sister Jemma and brother Jack, who were all "blown away" with happiness for them.
They decided to wait until now to share their news publicly because "we just wanted to enjoy the moment for us," explained Jodie, whose antique Indian rose-cut cushion diamond ring was designed by her friend, jeweller Theo Fennell.
The pair couldn't be more delighted. "It's absolutely brilliant," said Jodie, 35, who has a two-year-old son Indio from her former relationship with Argentinian polo player Andrea Vianini.
"We are totally chuffed and on cloud nine."
Said David, whose 2012 book, Pathfinder: A Special Forces Mission Behind Enemy Lines, was a best-seller: "I've never felt like this before. I knew it was different from the moment I met Jodie."