The beloved British actor passed away at the age of 65 after suffering complications following heart surgery at University Hospital in Coventry, England.
He was known to millions as Vernon Dursley in the Harry Potter films, and co-star Radcliffe - who also appeared with Griffiths in a 2007 London stage production of Equus - has heaped praise on his pal for his support over the years.
In a statement, he writes: "Richard was by my side during two of the most important moments of my career. In August 2000, before official production had even begun on Potter, we filmed a shot outside the Dursleys', which was my first ever shot as Harry. I was nervous and he made me feel at ease.
"Seven years later, we embarked on Equus together. It was my first time doing a play but, terrified as I was, his encouragement, tutelage and humour made it a joy. In fact, any room he walked into was made twice as funny and twice as clever just by his presence. I am proud to say I knew him."
Griffiths' Withnail & I co-star Richard E. Grant has taken to his Twitter page to pay his respects to the actor, who played Uncle Monty in the 1987 black comedy.
He posted several photos from their time on the set of the cult British movie and writes: "My beloved 'Uncle Monty' Richard Griffiths died last night. Chin-Chin my dear friend."
A slew of other celebrities have also taken to their Twitter accounts to mourn the star, with Snow White and the Huntsman actor Sam Claflin writing: "RIP Richard Griffiths. My lord, such a shame. hero", and British actor John Simm adding: "RIP the Mighty Richard Griffiths. Very Sad news indeed."
In reference to Griffiths' 1990s TV police drama Pie in the Sky, Matt Lucas told his followers: "Pie is now in the sky. So sad. Brilliant actor."
Russell Tovey, who appeared with Griffiths in Alan Bennett play The History Boys, shared: "Really sad. Our mate and leader has moved on to the theatre in the sky. We will miss you so much Richard Griffiths. RIP you wonderful man."
Thea Sharrock, who directed Griffiths in Equus, Heroes and Sunshine Boys, adds: "I worked with Richard more times than any other actor. Everybody knew he was my favourite. He was the most tender, gentle, kind, generous, loving man. His curiosity was unending, as was his striving for perfection. I cannot imagine a world without all those stories. I will miss him so very very much."