In a touching tribute, Quinto, 38, called the actor a "tremendous artist."
"We actually lost Leonard a year ago on the 27th of this month, so much love to him and his family, of course, always," he said while appearing on The Late Show this week.
Nimoy earned a place in Hollywood history for his portrayal of Spock in the original Star Trek films, and Quinto said he was honored to have the opportunity to get to know Nimoy while reprising the role in the reboots.
"I've never met somebody, actually, who fully embodied a sense of fulfillment in their life," Quinto said. "I really haven't. He was such a tremendous artist, philanthropist, and generous person and so intelligent. I miss him all the time. I really miss him so much at this point, obviously, marking the anniversary of his passing."
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The actor currently stars in the Off-Broadway play Smokefall, and said that Nimoy's wife and family came out to support him at the premiere.
"He was one of the greatest gifts my career has brought into my personal life, for sure," Quinto said. "His wife was at our opening night of our play. She came from L.A. to be there with us. She's as much a part of my life as he was. I feel very lucky to have known him on so many levels, for sure."
Nimoy passed away in Feb. 2015 after a long battle with chronic obstructive pulmonary disease. He was 83.