The 69-year-old singer, Morrison, received the award for his "outstanding creative works", reported Telegraph.
Gaga, 29, was presented with the award by her 88-year-old singing partner Tony Bennett.
The "Born This Way" singer performed a version of Linda Perry's "What's Up", before presenting her idol with Songwriters Hall of Fame inductee award.
Perry then returned the favour, performing a slowed down rendition of Gaga's "Bad Romance", before she was given her award by Bennett.
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