Sherman's son, Jeff, passed the news of his death along via Facebook.
"I have very sad news to convey," he wrote. "My Dad, Robert B. Sherman, passed away tonight in London. He went peacefully after months of truly valiantly fending off death. He loved life and his dear heart finally slowed to a stop when he could fight no more."
Born in 1925, Sherman fought in World War II and became a songwriter upon returning home. He helped write "Tall Paul" with his brother, Richard, which became a top-ten hit for Annette Funicello. The attention got the Sherman brothers a staff position at Walt Disney Studios, where they wrote "It's a Small World (After All)" and won two Oscars for "Mary Poppins." They also wrote songs for "Chitty Chitty Bang Bang," "The Jungle Book," "Charlotte's Web," "The Many Adventures of Winnie the Pooh" and both versions of "The Parent Trap."
Sherman was nominated for nine Academy Awards, winning two for "Mary Poppins." His last nomination came in 1979.
No cause of death is immediately known.