The singer tweeted the news on Thursday 14 April and revealed her son's name.
"Our little baby boy has arrived," she wrote. "Remington Alexander Blackstock was born 4/12/16 and he is healthy.
"We couldn’t be happier or more in love."
The 33-year-old, who is also mum to 22-month-old River Rose, announced she was pregnant for the second time in August 2015.
During one of her concerts in LA, she stopped as she was singing and said: "I was not planning on announcing this but I’m totally pregnant."
In November, Clarkson revealed she was suffering from sickness during her second pregnancy.
"I’m familiar with all-day sickness," she said on American chat show CBS This Morning.
"I have to get IVs and fluids because I get so dehydrated. It’s really bad."
Clarkson married Blackstock in October 2013. He already has two children, Savannah, 13, and Seth, nine, from a previous marriage.