He was 73.
Rogers was a founding member of the Miracles, the group once led by singer/songwriter Smokey Robinson, who quit the band to go solo in 1972.
Rogers was the only original member of the band left performing with the Miracles when he retired in recent years due to illness, the News said.
He was inducted into the Rock and Roll Hall of Fame as part of the Miracles last year, but wasn't well enough to attend the April ceremony.
"My cousin Bobby, who was like a brother to me, lost his battle and succumbed today," former Miracles member Claudette Rogers Robinson said in a statement to the newspaper Sunday. "He has gone on to be with his Lord and savior, Jesus Christ. Bobby will be missed and mourned by many."
Rogers is survived by his wife Joan, and children Bobbae Rogers, Gina Hughes, Kimberly Hughes and Robert Rogers III. He was predeceased by his daughter Robin Yopp, the News said.