"The babies are both healthy and resting -- Thanks to everyone for their love and prayers."
The newborns join Hannah, Deanna's 13-year-old daughter from a previous marriage, and Griffin, the couple's 11-year-old son.
According to the band's website, Chris and Deanna used in vitro fertilization to conceive and had then embryos transferred to a gestational surrogate since Deanna had a partial hysterectomy in 2006. The couple, who wed in 2000, had announced the pregnancy in May.
The rocker said he is thankful to his fans and couldn't be happier about the birth of his new children.
"Deanna and I are overjoyed about this double blessing," Chris said. "Thank you for your expressions of love and support and for respecting our privacy during this special time."
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