Better known as Mike D, the musician - a singer, rapper and drummer - left a tribute for Yauch on the iconic hip-hop group's Facebook page.
Copyright: Rex Features Everett CollectionDiamond said of his bandmate: "I know, we should have tweeted and instagrammed every sad, happy and inspired thought, smile or tear by now.
"But honestly the last few days have just been a blur of deep emotions for our closest friend, band mate and really brother."
The 46-year-old added: "I miss Adam so much. He really served as a great example for myself and so many of what determination, faith, focus, and humility coupled with a sense of humour can accomplish.
"The world is in need of many more like him. We love you Adam."
Diamond's statement follows that of fellow Beastie Boys member Ad-Rock, who thanked fans for support yesterday.
Yauch, who died aged 47, had been fighting a three-year battle with cancer.
Watch the video for classic Beastie Boys track '(You Gotta) Fight for Your Right (To Party!)' below: