The 68-year-old actor and his daughter, 22, shared a heartfelt message on Instagram late New Year's Day.
"We love you, and Happy New Year!" they said simultaneously in the short video, while seated across what looked to be a restaurant table.
Actress and friend Sharon Stone was among the first in the commenters, who wrote back to the father and daughter, "Love you too 😍"
The family's celebratory wishes come a little over a week after John posted a festive Christmas video, along with Ella and his 12-year-old son, Ben Travolta.
The Paradise City actor shared Ben and Ella with late wife Kelly Preston, who died at age 57 in July 2020 after being diagnosed with breast cancer. The couple were also parents to son Jett before he died at age 16 in 2009.
John's Christmas clip documented the actor, with Ben's dog Peanut perched on his knee, and his children wishing fans a happy holidays.
"Merry Christmas everyone! 🎄," he captioned the video.
A month earlier, Peanut made a hilarious appearance in the family's Thanksgiving video, in which the dog jumped on the Grease star and gave him a quick kiss before running off-screen.
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John shared the sweet adoption news last spring with a photo of Ben holding the pup, in which the Pulp Fiction star smiled behind them.