Rod Stewart's Son Sean Stewart Marries Jody Weintraub in Las Vegas: Source

Rod Stewart's oldest son Sean Stewart is now married, PEOPLE confirms exclusively.

The entrepreneur, 42, proposed to his girlfriend Jody Weintraub, also 42, on Valentine's Day during a trip to Las Vegas last week and the duo headed straight to the courthouse the same night.

"Sean asked her while they were out to dinner at Catch. They married shortly after getting their marriage license at 10 p.m. at Little Church of the West," a source close to the couple exclusively tells PEOPLE.

The Dirty Weekend streetwear designer has known the former EXTRA producer, daughter of the legendary late producer Jerry Weintraub, since high school, the source explains. "They are both very family-oriented people."

The Malibu-based producer — who will be taking the Stewart name — is a proud mom to her 5-year-old son Doc, who is a big fan of Sean and vice versa. "They go to the beach, he reads him books, he takes him to karate class, they play Magna-Tiles," the source shares of the boy's new stepfather, adding, "They're cute together!" Things with Jody and her ex-husband are amicable. "There's no drama," the source notes.

As for the last-minute nuptials, the couple intended on just taking a typical romantic trip for Valentine's Day to the Wynn hotel, but then it quickly turned into a lifetime commitment. "Sean and Jody share a best friend, Courtenay Semal, which was the reason why they kept reconnecting over the years. They both have famous families, they just get each other," the source shares, noting that the couple is "so much alike" and are "born two days apart" from one another.

After Sean's sweet proposal, he called his mom Alana Stewart on the way to the courthouse and the source says that it took her a minute to really know if he was serious or not, "as he's known as a bit of a jokester in the family."

When they sent her photos and videos after they made it official, "she cried" and was "so so happy for him." Sean also talked to his dad, Rod, who was heading to Tampa to play an intimate show at the Hard Rock Hotel & Casino. "His dad was so happy to hear the news," the source says.

For the casual ceremony, Sean wore jeans and a YSL sweater, while the bride rocked a black, cashmere jumpsuit. "They just went back to the hotel after. It was kind of like, 'Holy s---, we just got married,' but they were so so excited and didn't regret one thing. Their relationship and connection is solid."

When the couple got back to Los Angeles, they celebrated with Rod and Alana at Nobu in Malibu. Sean's parents married in 1979, then divorced in 1984. Rod is now married to his wife of 14 years, Penny Lancaster.

Out of the Stewart clan, Sean has an older sister Kimberly, 43, younger half-sisters Ruby, 35, and Renee, 30, younger half-brothers Liam, 28, Alastair, 17, and Aidan, 12, and an older half-brother, Ashley Hamilton, 48, from his mom's marriage to Golden Globe-winning actor George Hamilton.

The entire crew will officially be celebrating the newlyweds — who are already looking for a home together — soon as they plan on having a traditional wedding this summer in Spain at Marbella Beach Club with their families.

Fans of the Stewart family may also remember Sean from the reality television show, Sons of Hollywood, in which he starred alongside celebrity sons David Weintraub (who has no relation to Jody) and Randy Spelling.

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Despite Sean's famous upbringing, he's poured his heart and soul into his recent business endeavors and getting his clothing company Dirty Weekend off the ground, and will be "rebranding the apparel company next week," the source says of his focus.

With his new wife, Sean is "proud" to finally have a family of his own, and he and Jody plan to have children together.

"They're the same person," the source says of the couple and why it works. "They're from the same town, they have the same friends. They just understand each other."