David passed away at the age of 91 on Saturday (September 1) due to complications relating to a stroke.
He and songwriting partner Burt Bacharach penned many of the biggest hits of the 1960s and 1970s, including 'Close to You', 'I Say a Little Prayer' and 'What's New Pussycat?'.
Warwick - who sang Bacharach and David's 'Walk on By' - has praised the writer's influence and gentle nature in a statement to CNN.
"I feel as if I have lost another family member, but knowing I will always have him with me each time I sing the lyrics written for me by him will continue to bring me a sense of him being with me always," she commented.
Kristin Chenoweth, Herb Alpert and Smokey Robinson are among the other stars who have honoured David's life and legacy.
Earlier this year, Bacharach and David were given the prestigious Library of Congress Gershwin Prize for Popular Song at a White House gala hosted by US President Barack Obama.
Watch Dionne Warwick sing 'Walk on By' below: