The musician was one of the big names selected by museum officials in May (14) but he skipped the ceremony in New York City after his sibling Joyce passed away.
The Waterloo Sunset hitmaker accepted the honour via video, and he also took to Facebook.com to write, "I am profoundly honoured to have been inducted into the American Songwriters Hall of Fame and disappointed not to have been at the event in New York but I felt it necessary to be near my family at this sad time of my sisters (sic) funeral.
"I wish to thank everyone at the Songwriters Hall of Fame who voted for me and give a special thanks to all the loyal Kinks fans who have stood by us all these years. I hope to repay such loyal support by trying my best to continue to write songs in the future that are worthy of such an accolade."
Jon Bon Jovi was on hand to pay tribute to Davies at the ceremony, performing his hits You Really Got Me and All Day and All of the Night at the end of the show.
Other acts honoured included Scottish singer Donovan, Graham Gouldman of the band 10cc, singer/songwriter Mark James, who penned Elvis Presley's Suspicious Minds, and Jim Weatherly, who is known for writing Gladys Knight & The Pips hits Neither One of Us and Midnight Train to Georgia.
Performers such as Miguel, Chita Rivera, Chubby Checker and Jackie Evancho also took to the stage at the event.