The proposal took place in her hometown of New York City on Thursday evening, PEOPLE has learned.
Carey, 45, and Packer, 48, – an Australian businessman – first met at the Hercules premiere "a few years ago", she told Steve Harvey last year.
They made their red carpet debut in September last year at The Intern premiere in New York City after being photographed getting cozy while on an Italian vacation in June.
Shortly before Christmas, the couple headed to Aspen, Colorado with the singer's 4-year-old twins Monroe and Moroccan with ex-husband Nick Cannon.
This will be the third marriage for Carey, who was also previously married to music executive Tommy Mottola. Packer has three young children with his ex-wife Erica Baxter.
E! News were first to report the engagement.