"Patrick and I are over the moon in love with our son Rhys James Carney... born August 28th, 2018," Branch wrote on Instagram Thursday.
Rhys was born at 11:48 p.m., weighing in at 8 pounds, 13 ounces. Rhys also measured 20 inches long.
Carney also shared the same post on his Instagram page.
Branch and Carney announced they were expecting in February, with an Instagram post. At the time, they were preparing to send out the Save the Dates cards for their wedding.
"Well, we were just about to send out Save the Dates for our wedding in May when we got this little surprise," Branch, 35, wrote alongside video of her ultrasound. "Wedding is postponed and Baby Carney is happening this summer! Patrick and I couldn't be more excited! xx."
Branch and Carney got engaged on her 34th birthday in July 2017. She shared a photo of the ring, adding, "Thank you for all the birthday love and wishes. Last night, right before I blew out my candles, [Carney] asked me to marry him and then I had nothing left to wish for. 34 might be the best year yet."
Rhys is Branch's second child. She also shares 12-year-old daughter Owen with ex-husband Teddy Landau.
Carney recently worked on Branch's third album, Hopeless Romantic.
"We've definitely talked about doing a project together that wouldn't be a Michelle Branch record, which is exciting, because at this point I don't know what that sounds like," Branch told Entertainment Tonight last September. "I guess it's just kind of one of those things that we're gonna take song by song. Some of those are definitely more Michelle Branch songs, but I guess it's one of those things where we'll know the second we start working. Whatever inspires us more and pulls us more, will probably be what we'll record and what we'll spend time on."
Branch also said the couple does not plan on getting a wedding band.
"It was funny, because I was talking to our wedding planner, and she was asking if we wanted a live band at the wedding, and I was like, 'No!'" Branch told ET. "She was surprised. I was like, 'The last thing we want at our wedding is live music.'"
"I mean, unless it could be, like, Led Zeppelin," Carney joked. "I just don't want a wedding band."
Branch is best known for her hit "The Game of Love" with Santana, "Breathe" and "Are You Happy Now?" Hopeless Romantic was released in April 2017 as her first album since 2003.
Photo credit: Gregg DeGuire/WireImage