The 72-year-old, who is the father of actress Angelina Jolie, was spotted in London last month sharing an ice cream cone with two of his grandchildren, Pax and Zahara.
Voight recalled the experience in an interview with Access Hollywood, admitting that he was surprised the moment was photographed.
"I didn't know they recorded that," the actor said.
Voight continued: "I love my grandchildren. [I'm a] very, very happy granddad."
Jolie's partner Brad Pitt recently surprised his children with Shetland ponies, which are being kept at the couple's Chateau Miraval estate in the south of France.
Last year, Voight praised Jolie and Pitt's children for being beautiful and bright, noting that Shiloh is particularly wise beyond her years.
Watch Jon Voight winning an Oscar for his role in Coming Home at the 1979 Academy Awards below: