The pair, who are said to be living together in former One Direction star's LA mansion, have been dating since earlier this year.
Posting a photo of Liam, 22, lying on the sofa with the pet on Instagram, Cheryl, 33, wrote,"Our new family member, he is beyond cute. The dog is adorable too @toosmallforteacups thank you."
Abbie Sisson, who helped the couple find the puppy its new home, also expressed her excitement on Instagram.
"Both my little chocolate drops have now gone to their new loving and wonderful homes once again with such lovely people @cherylofficial," Sisson wrote.