Smart, 25, tweeted the news on Thursday, January 17.
"Introducing the new addition to the family... Welcome home," he wrote alongside a picture of a little brown boxer.
Lopez, mother to four-year-old twins Max and Emme, her kids with ex-husband Marc Anthony, retweeted her beau's announcement, with an added note about the pup's name, reported US magazine.
"So happy! LilBabyBear. Could get confusing!" she wrote.
'Bear' is their pet name for each other. Both Lopez and Smart have used it in the past as a term of endearment on Twitter.
"BEAR!!!!!!!!!!!!!! Today is OURS!!" the "Dance Again" singer, 43, wrote on the micro-blogging site for her one-year anniversary with Smart in October.
"Thank you for sharing your beautiful smile with me everyday!"
Smart responded, "Happy 1 year anniversary to the most gorgeous, kind, sweet, funny, beautiful lil Bear in the world..."