Alexis Bledel and Vincent Kartheiser Finalize Divorce Less Than 3 Weeks After Filing: Reports

Alexis Bledel and Vincent Kartheiser's divorce has reportedly been finalized.

The official end to the couple's marriage comes just 20 days after PEOPLE confirmed that the Mad Men alum filed for divorce from the former Gilmore Girls star on Aug. 10. (Bledel's rep and the New York's Putnam County Court both corroborated the filing at the time.)

Reps for Bledel and Kartheiser did not immediately respond to PEOPLE's request for comment the final status of the divorce, which was first reported by Us Weekly and later by Page Six and OK. A legal rep for Bledel declined to comment.

RELATED: Vincent Kartheiser Files for Divorce from Alexis Bledel After 8 Years of Marriage

Charles Sykes/Invision for the Television Academy/AP Alexis Bledel and Vincent Kartheiser

Bledel, 40, and Kartheiser, 43, met on the Mad Men set in 2012. Kartheiser played Pete Campbell, and Bledel appeared in season 5 as Campbell's mistress Beth Dawes.

Shortly after Bledel appeared on the show in 2012, the couple were spotted kissing. They privately tied the knot in 2014.

RELATED: Alexis Bledel and Vincent Kartheiser's Not-So-Secret Love: A Brief History of the Couple's Uber-Private Life Together

Bledel and Kartheiser have kept their relationship private, rarely making public appearances together or speaking about each other in the press. The pair also avoids use of social media, so personal posts of their relationship can't be found.

Kartheiser expanded on this mindset in a conversation with Vulture. "It's something I realized about the most important things in my life," Kartheiser said in 2014. "If I share them with the world and I open that door to their fuming anger that they need to get out or their adoration that they want to flaunt, it lessens it. It cheapens it; it weakens it. And it's magical, love, and all of that is profoundly spiritual, and it just doesn't feel right."

HBO Alexis Bledel and Vincent Kartheiser on Mad Men

Bledel and Kartheiser welcomed their first child in fall 2015 but kept the pregnancy and birth a secret. Their reps confirmed the baby's arrival to PEOPLE.

While the celebrity parents still haven't introduced their child to the world, Bledel's former Gilmore Girls costar Scott Patterson had some insight into her life as a mother.

"She's really blossomed as a woman and now she's a proud new mother and married and happy," Patterson told Glamour. "We're comparing notes because my son [born July 2014] is about a year and a half older than her young son. I'm showing her photos and videos and what to expect. We're just really enjoying each other's company."