Hudson, 36, Instagrammed video of herself listening to Franklin's cover of The Beatles' "Let It Be."
"I have no words, so I will let the Queen say it!" Hudson wrote. "But I will say while teaching me about your life, u taught me so much about life and schooled me in mine. I will never forget those teachings #riparethafranklin."
Davis paid his own emotional tribute to Franklin on Thursday, Instagramming a throwback pic of the two together.
"I’m absolutely devastated by Aretha’s passing," he wrote. "She was truly one of a kind. She was more than the Queen of Soul. She was a national treasure to be cherished by every generation throughout the world. Apart from our long professional relationship, Aretha was my friend. Her loss is deeply profound and my heart is full of sadness."