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The couple, who met on the tennis circuit, have been dating for almost five years.
Announcing the news on Instagram, external with a photo of the ring, world number 24 Boulter wrote: "We've been keeping a small secret."
Great Britain face Australia in the United Cup, external in Sydney on 1 January, with Boulter, 28, and 25-year-old De Minaur named in their respective teams.
With two singles matches and a mixed doubles tie in every fixture, Boulter and De Minaur could play against each other if selected for the doubles.
"I wouldn't say I was thrilled at the idea of playing him all over again," Boulter said before news of the engagement.
"He's a top-10 player and he knows how to play tennis, so there's one side of it.
"Then there's the personal side of it, which is difficult but also great for bragging rights."
Playing together, Boulter and De Minaur reached the second round of the mixed doubles at Wimbledon last year.
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