Williams, 43, has immortalised the actor with a stick-man design, which references Moore's 1960s television series "The Saint", reported Daily Mirror.
Fans noticed the inking - located on his upper right arm - at his Southampton tour date this week, while he performed in a kilt and short-sleeved T-shirt.
Moore and Williams first met at a charity event for UNICEF in October 2016 and set social media alight with a backstage picture.
Posing together in their dressing rooms, Moore captioned the snap: "Very pleased to meet up with fellow UNICEF ambassador robbiewilliams. A good man."
The lyrics include: "Why'all know who I am, I'm still the boy next door, that's if you're Lord Litchfield and Roger Moore. If I've gone up in the world, or is the world gone down on me, I'm the one who put the Brits in celebrity".
Williams, who also has tattoos honouring Ronnie Corbett, The Beatles and Jesus Christ, got the tattoo just weeks after Moore's death was announced on May 23.