"The process isn't done yet and we're thankful for the love, support, and respect for our privacy that has been offered to us," Pete Buttigieg says

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Pete Buttigieg and Chasten Glezman
Pete and Chasten Buttigieg
| Credit: KAMIL KRZACZYNSKI/AFP via Getty

Pete Buttigieg and husband Chasten Buttigieg have expanded their family.

The 39-year-old U.S. Secretary of Transportation and teacher/author Chasten, 32, announced the news on social media Tuesday, sharing the statement, "For some time, Chasten and I have wanted to grow our family. We're overjoyed to share that we've become parents!"

"The process isn't done yet and we're thankful for the love, support, and respect for our privacy that has been offered to us. We can't wait to share more soon," they added.

Pete and Chasten tied the knot in June 2018. Back in September, the couple opened up to PEOPLE about how they met and their desire for welcoming kids into their family, which they've been open about in the past.

"We're just navigating those conversations," Chasten said at the time of family planning. "I'm so glad that we get this time ... And it's allowed us to have conversations, those necessary conversations, and now it's really overwhelming figuring out how and where and when, and how much — my God."

"But luckily, we have a lot of friends who've had families in very different ways," he continued. "So we've just been having great conversations with our friends about how they figured it out, and we'll go from there. We're just really excited and overwhelmed, I think."

"Very excited," added Pete. "It's one thing when you're in the middle of a campaign and there's just no room for anything else. Not that there'll ever be an easy or simple time. I don't think there is for anybody, but it's time to take those steps."

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Buttigieg became a political star seemingly overnight when he became the first openly gay presidential candidate, after he announced his longshot presidential bid in April 2019, shortly before the ultimate winner, President Joe Biden, made his own campaign announcement.

Back in February 2020, while still on the campaign trail, Pete told PEOPLE that "no matter what happens, I think the next chapter in our personal lives is going to be about kids." He said he was "really excited" about fatherhood and that "Chasten is just especially wired to be a great parent."

"We would hope to do [it] soon," added Pete. "One way or the other."

RELATED VIDEO: Pete and Chasten Buttigieg Tell Their Love Story: 'Hallmark Movie' First Date, Double Proposals and What's Next

In June, Pete got candid about coming out and shared the piece of advice he'd give his 13-year-old self during an interview with MSNBC's Jonathan Capehart.

"At 13, I was beginning to understand that I was different — no, not understand. I was beginning to perceive that I was different and not understand," he recalled. "The understanding that I had to gather was the task of years and years."

"I guess, it would've been nice to hear, 'There's nothing wrong with you. Just hang in there,' " continued Pete.

"Thirteen-year-old Pete came out alright," he added. "I want to make sure 13-year-old 'whoever you are out there' knows to hang in there, that — not to say it will be easy — but there's a lot of people rooting for you, including the president and people like me."