The Skyfall star was widowed in 2001 after the death of her husband Michael Williams. The couple were married for 30 years before Williams lost his battle against lung cancer.
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Dench first sparked rumours of a romance with Mills last year but has now confirmed the reports.
The 77-year-old told Yours: "When you've been widowed a long time it's very, very nice to have the company of somebody.
"It doesn't have to be a great, passionate sexual affair but it's nice to have someone who says, 'I'll find your keys for you', or, 'Let's go to the theatre tonight'. Very nice."
It was revealed last month that the actress will star alongside Steve Coogan in Stephen Frears's new film Philomena.
Watch Dame Judi Dench in the trailer for Skyfall below:
