The British model has been on "cloud nine" since her ex-army beau popped the question four months ago following a whirlwind romance.
She gushed to Britain's HELLO! magazine: "It is absolutely brilliant. We are totally chuffed and on cloud nine."
David added: "I am feeling really excited and over the moon. I've never asked anyone else to marry me - I've never felt like this before."
The couple decided to keep their engagement a secret at first so they could revel in the happy news with their close family and friends.
Jodie, 35, added: "We just wanted to enjoy that moment for us, although we told our immediate families. I can't believe we got away with it."
David - who has served in the military for over 19 years - chose Udaipur in Rajasthan, India, as the location for his proposal after being invited to give a talk on leadership and war over there, and was nervous about Jodie foiling his plan on the flight over.
He joked: "I hid [the ring] in a pair of socks and panicked at one point when she very nearly did find it."
Jodie - who has a two-year-old son Indio, with her ex-partner Andrea Vianini - believes she has found The One in David and instantly knew he was the man she wanted to spend the rest of her life with.
She said: "It feels totally right when you meet the right person and you realise then why previous relationships didn't work. David and I are the same age and we've both been through a lot. We're older and wiser and feel very lucky to have found each other.
"I'm super happy after going through so many years op trauma and unhappiness. He is going to be a fantastic stepdad. They bonded from day one and it's lovely to see Indi have a bit of male stability."