Pete Buttigieg and his husband have announced the birth of adopted twins.

In a post to social media on Saturday, the US transportation secretary and former candidate for the Democratic presidential nomination said: “Chasten and I … are delighted to welcome Penelope Rose and Joseph August Buttigieg to our family.”

The Buttigiegs announced last month that they were engaged in the adoption process. Sharing a picture of the babies on Saturday, they said they were “beyond thankful for all the kind wishes since first sharing the news that we’re becoming parents”.

One of the twins is named for Buttigieg’s father, Joseph, a Notre Dame professor who died in 2019.

Buttigieg, 39, is a former mayor of South Bend, Indiana who came from obscurity to make a strong impression in the Democratic presidential primary in 2020. He is now the first out gay parent in the US cabinet, having already become the first openly gay person to be confirmed by the US Senate for a cabinet post.

The Washington Post reported in July that the Buttigiegs had put themselves on lists to adopt a baby or babies abandoned or surrendered, and were preparing by “going through home studies and parenting workshops, writing up descriptions of their family values and ideal weekends”.

Chasten, a part-time drama school teacher, described how he received a call about a mother in labour wanting to place her baby for adoption. The mother then changed her mind.

“It’s a really weird cycle of anger and frustration and hope,” he said.

The couple met in 2015 on the dating app Hinge and married three years later. After being appointed to the Biden cabinet, Pete Buttigieg said: “Travel in my mind is synonymous with adventure, growth and even love, so much so that I proposed to my husband, Chasten, in an airport terminal.

“Don’t let anyone tell you O’Hare [the Chicago airport] isn’t romantic. And let me take this chance to thank Chasten for all that he does, and for his sacrifices, to support me in pursuing public service.”

When Pete Buttigieg announced that he and Chasten were looking to adopt, first lady Jill Biden shared his tweet and said: “Congratulations to you and Chasten! Welcome to parenthood!”

The interior secretary, Deb Haaland, said: “Being a parent has been one of the great joys of my life. Congrats to you and Chasten on this terrific news!”

Lis Smith, Buttigieg’s top communications adviser during his presidential bid, said: “They will be the best dads.”

On Saturday the Minnesota senator Amy Klobuchar, once a rival for the Democratic nomination, tweeted: “You’re both going to make wonderful parents, congrats.”