Robert B Sherman, who has died aged 86, was part of one of the most unusual songwriting teams of all time. He and his younger brother Richard may not be as well known as other pairs of composers and lyricists, but they will for ever be remembered as the writers of Mary Poppins, The Jungle Book and a swath of other productions from Walt Disney Studios.

Their score for Mary Poppins (1964), the movie that introduced Julie Andrews to filmgoers, secured them a place in popular musical history and made them multimillionaires. Featuring songs including Jolly Holiday, Let's Go Fly a Kite and Feed the Birds, it won them two Oscars. It also included the classic A Spoonful of Sugar and the song with the one-word title that they used when they accepted the Academy awards: "All we can say is 'Supercalifragilisticexpialidocious'."

The Shermans were the sons of a Tin Pan Alley songwriter, Al Sherman, who, although he had written for Broadway shows including the Ziegfeld Follies, had found it difficult to make a living. When Robert was born, Al's biggest problem, he would say, was finding the money to pay his doctor's bill, but as he was contemplating the problem, he opened an envelope containing a large royalty cheque for the song Save Your Sorrow.

The two brothers were born in New York, but the family moved to Beverly Hills in 1937, and the boys attended the Beverly Hills high school. There, Robert began writing and producing radio programmes that were highly acclaimed by broadcasting professionals. At 16, he wrote a stage play, Armistice and Dedication Day, which generated thousands of dollars for war bonds. The US war department awarded him a special citation in gratitude.

He joined the army in 1943, at the age of 17. Two years later, he led a squad of men into the Dachau concentration camp, the first Americans to stumble on the horrors there, only hours after the Nazis had fled. During war service, in April 1945, he was shot in the knee, as a result of which he walked with a stick for the rest of his life. He spent much of his service in Britain, where he was stationed in Bournemouth and Taunton. It was this experience, he would say, that got him interested in British popular culture.

After the war, he attended Bard College in upstate New York, where he studied English literature and painting, wrote two novels and graduated in 1949.

The two brothers always worked as a team, sharing between them the job of writing both music and lyrics. Their first hit was the rock'n'roll single Tall Paul, sung by Annette Funicello, in 1959. Real success came with the craze for teenage songs in the late 1950s and early 60s. Their number You're Sixteen was a huge hit in 1960 for one of the short-lived idols of the time, Johnny Burnette. The same year they were taken on by Walt Disney as staff songwriters.

The first films they worked on were "live action" movies (as Disney films without cartoon characters were then called) including The Parent Trap (1961), In Search of the Castaways (1962) and Summer Magic (1963), and they also provided songs for the animation The Sword and the Stone (1963). For the 1964 New York world's fair, they wrote It's a Small World After All, which became the Disney "national anthem" and is now played regularly at Disney theme parks.

The Shermans were the obvious choice for scoring Mary Poppins. The film was to be acclaimed as "the best live action film in Disney's history" – although it did include some animation. The music was its best publicity vehicle. The soundtrack album reached number one in the US and stayed in the charts on both sides of the Atlantic for 18 months. The brothers won Oscars for best original soundtrack and best song, for Chim Chim Cher-ee, with the film winning three other awards, including Andrews for best actress.

In 1965, Robert and Richard were recruited to work on The Jungle Book (1967), Disney's animation inspired by the Rudyard Kipling stories. They replaced the original songwriter, Terry Gilkyson, whose songs Walt Disney considered too close in mood to the dark tone of Kipling's work. The Shermans produced seven new songs, written as "character numbers" to set each creature's place in the story, including Trust in Me (for Kaa, the serpent), That's What Friends Are For (sung by the moptop barbershop vultures), and I Wan'na Be Like You (for King Louie, the orangutan). Disney retained Gilkyson's The Bare Necessities, which was nominated for an Oscar. The Jungle Book was the last film produced by Walt Disney, who died before its release.

The Shermans stayed on with the studio for a few other projects, including Bedknobs and Broomsticks (1971) which, like Mary Poppins, combined live action with animation, and The Aristocats (1970). Chitty Chitty Bang Bang (1968) was their first non-Disney film and in 2002 also became a long-running stage show at the London Palladium, for which the brothers wrote several new songs. The film, for the James Bond producer Albert R Broccoli, won the pair their third Oscar nomination. There would be six more.

They also provided scores for Charlotte's Web (1973), Tom Sawyer (1973), The Slipper and the Rose (1976) and The Many Adventures of Winnie the Pooh (1977), among others. In 1974, they wrote the Broadway hit Over Here!, a show about troop entertaining, using the music styles of the 1940s. It ran for a year, and starred the then two surviving Andrews Sisters, Patty and Maxene. They returned to Disney in 2000 after 28 years to score The Tigger Movie.

Sherman, who lived in London from 2002, married his childhood sweetheart Joyce Sasner in 1953. She died in 2001. He is survived by his four children.

• Robert Bernard Sherman, songwriter, born 19 December 1925; died 5 March 2012

• This article was amended on 7 March 2012. The original stated that The Sword and the Stone was a live-action film. This has been corrected.