Liam Hemsworth and Miley Cyrus
06/07/2012 AT 09:45 AM EDT
and Liam Hemsworth
have the full support and blessing of their families in the wake of their engagement,
sources close to both sides tell PEOPLE.
"Billy Ray loves Liam. He's happy his daughter has found the right guy," one source says, adding that Hemsworth has spent a lot of time with her family, barbecuing together. "The whole family loves Liam."
Cyrus's mom Tish is also said to be "excited" by the news.
Likewise, Hemsworth's family in Australia has gotten to know Cyrus through their visits, and is happy for them. "They spend Christmas and other holidays together. They've been down to Australia," says a source.
The pop star, 19, and the actor, 22, got engaged May 31 following three years of dating, after meeting on the set of The Last Song
Though their daughter is still a teenager, Billy Ray and Tish reportedly aren't wistful or sad that she's growing up. "She's pretty independent already," says a source. "They're just so happy she's found someone who makes her so happy."
On Twitter, Billy Ray, 50, wrote
: "All I ever hoped for as a Daddy was to see my kids reach their dreams. To find happiness ... peace of mind ... and someday know ... true love."
For more on Cyrus and Hemsworth's engagement, including what their families think – and to see a photo of Cyrus's ring – pick up this week's issue of PEOPLE, on newsstands Friday
Reporting by JD HEYMAN