The 'We Belong Together' singer welcomed a son and a daughter with husband Nick Cannon on Saturday, April 30, a date which also marked the couple's third wedding anniversary.
"I wish I could personally thank all those around the world who continue 2 send congrats+prayers for #dembabies! they're doing great (sic)," wrote Carey on her Twitter account.
"And they are the most incredible gifts we could ever have imagined!"
The diva also teased that she and Cannon are preparing to disclose the names of their children, asking her Twitter followers for their guesses ahead of the official announcement. She told one follower that the names each begin with M but declined to reveal any further details.
It was previously announced that the baby girl was born first, weighing 5lb 3oz, followed by the baby boy, who weighed 5lb 6oz.
Carey and Cannon have also confirmed that they renewed their wedding vows with Reverend Al Sharpton at the hospital over the weekend.
> Carey, Canon congratulated by stars
Watch Mariah Carey's music video for 'We Belong Together' below: