The pair got engaged during a helicopter ride over New York City, with Windsor's recent Strictly partner Lisa Riley present for the proposal, The Mirror reports.
Windsor and Riley became close friends during their time together on the 2012 series and reached the semi-final stage of the competition.
The couple are reportedly hoping to marry next summer in a Broadway-themed celebration.
Windsor revealed: "I'd been planning the proposal with Lisa's help since March. It was absolutely the most romantic thing I could ever think of.
"Everyone on Strictly was thrilled for us. Of course it would be absolutely amazing if Bruce got up and did something but we'll have to see!
"Davide's always wanted to learn the Argentine tango but annoyingly it's not my forte so I'm hoping to get a bit of help from Flavia or Vincent."
The newly engaged couple celebrated their engagement alongside Riley with champagne at Manhattan's Soho House.
Windsor, 33, is returning to the BBC dancing series this year, despite changes being made to the professional lineup.
However, it was previously announced that pro favourites Aliona Vilani, Vincent Simone, Flavia Cacace, and Erin Boag will not be returning to the show.
Strictly Come Dancing returns to BBC One next month.
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