Kourtney Kardashian and Travis Barker 'Feel Complete' After Welcoming Baby Boy: Source

The couple welcomed their first child together and a source tells ET they're enjoying every moment.

Kourtney Kardashian and Travis Barker couldn't be happier after welcoming their first child together.

A source told ET on Tuesday that Kourtney and Travis "feel complete after the birth of their son."

"The couple can’t stop smiling and expressing gratitude for their blessing," the source continued. "The couple has been surrounded by love and their families have been there to support them where needed. Right now the couple is trying to enjoy this time, because they know it goes by fast."

Another source confirmed to ET on Monday that the couple had welcomed a baby boy, noting, "Kourtney gave birth and she and Travis are so elated. They're feeling extremely fortunate that both Kourtney and their baby are healthy after the complications Kourtney went through."

"They recognize that the circumstances could have been a lot different, so they are feeling extra appreciative and grateful that everyone is safe, happy, and healthy," the source added. "That is what’s most important to them."

Last month, Kourtney was put on bed rest as she neared her due date, and in September she had to undergo fetal surgery, saying that it saved her son's life. The reality star opened up about her health concerns in a recent interview with Vogue.

"[Geriatric pregnancy] is just so wild. But my doctors are so cautious, and I've had so many more restrictions than my other pregnancies," Kourtney said. "The first trimester was no working out, no flying on airplanes, no sex. Then the second trimester, I could do anything. Now, I am back to all the restrictions."

"I've finally been able to let go of the fear and worry that everybody else put in us because of this pregnancy," she added. "I'm ready to go in, have the baby, and have the experience we're meant to have."

ET's source said that while there were "naturally worries and anxieties," now Kourtney and Travis "feel like they can take a step back, breathe, and enjoy."

"They are taking things day by day and looking forward to this new chapter outside of their lives as a married couple," the source continued. "They can’t wait to build a new life and make memories together as a bigger family."

The couple haven't officially shared the news of their baby boy's arrival, but Barker dropped hints about a possible name in a recent podcast appearance, sharing that the couple planned to name their son Rocky Thirteen.

The new baby is the Travis and Kourtney's first child together, but will actually be No.7 in the Kardashian-Barker blended household. Kourtney shares three children, Mason, 13, Penelope, 11, and Reign, 8, with her ex, Scott Disick, while Travis is the father of Alabama, 19, and Landon, 17, whom he shares with his ex-wife, Shanna Moakler. He also helped raise Atiana De La Hoya, Moakler's 24-year-old daughter, whom she shares with her ex, Oscar De La Hoya.