The baby boy is the first child for both Morris, 26, and her longtime boyfriend, Taylor Hubbell, whom she met in high school.
In an interview with Fitness magazine in 2011, the former Beyonce backup dancer gushed about her future plans to have a family with Hubbell.
"I want to marry Taylor and have kids with him," she said. "I love acting, but if it affects my relationship, then I won't continue."
News of Morris' pregnancy broke in April when a source told Us Weekly the couple were "incredibly happy and excited."
"Heather is glowing! She is so happy. She is really excited to be a mom," a second source told the magazine. "She is just amazed by the whole experience."
Morris did not return for the fifth season of "Glee."