"Thank you for all the well wishes for Rachel and the baby. Rachel and our baby boy are both healthy and doing well. They are recovering at UCLA," Brendon, 40, tweeted.
"I am sure it will not be too long until Rachel shares some pics, but I will leave that up to our momma warrior. No name as of yet!"
Rachel, a former Big Brother winner, announced the sex of Baby No. 2 in early September.
"It's going to be so fun to have a girl and a boy! Adora is going to teach her baby brother so much and I can't wait to meet him!" Rachel gushed to People at the time, admitting that she "totally wanted a baby boy."
"OH Baby!!! WELCOME BRENCHEL BABY #2! Happy Mother's Day! We have a lot to celebrate this year. As a mom it's my day to celebrate Adora & OMG baby #2!!" Rachel captioned a family photo of them celebrating outdoors amid the ongoing coronavirus pandemic.
In the photo, Rachel was gently cupping her noticeable baby bump in a floral-print dress, and she added, "I can't believe I'm pregnant!... I can't wait for what this pregnancy has in store for us!!!!"
In her Mother's Day post, Rachel also revealed she and Brendon had been "trying for awhile to have another" child after welcoming their now four-year-old daughter Adora Borealis in April 2016.
"I'm already planning their reality TV appearances," Rachel joked of her kids in an interview with People.
But Brendon said at the time he was just concerned about keeping Rachel and the baby healthy since coronavirus was spreading rapidly across the country.
Rachel and Brendon first met when they competed on Big Brother's twelfth season in 2010.
After beginning a "showmance" during the competition, the couple continued dating and got engaged on Valentine's Day before returning to Big Brother in Summer 2011 as part of the thirteenth season's "duos" twist in which three pairs of former houseguests were given a second chance to compete on the show.
While Brendon was evicted -- twice -- from the Big Brother house midway through the competition, Rachel made it to the Season 13 finale, where she took home the show's $500,000 grand prize after winning a 4-3 jury vote over fellow contestant Porsche Briggs.
The couple then made their third appearance on a CBS reality series when they competed on The Amazing Race's 20th edition in early 2012.
They finished the season's final leg in third place.