Richard Sherman said he and his brother aimed for a jazz sound, with a Dixieland-like melody. He added that "When we first got an idea for 'I Wan'na Be Like You,' we said an ape swings from a tree, and he's the king of apes. We'll make him 'the king of the swingers.' That's the idea, we'll make him a jazz man." Once Prima was invited to do the song, he mockingly responded to the Shermans with "You want to make a monkey out of me? You got me!" The instrumentals were originally recorded by Prima—who also played the trumpet—and his band, Sam Butera & The Witnesses, but the music was replaced by one written by the film's composer, George Bruns, and orchestrated by Walter Sheets. The "scat dialogue" between Baloo and King Louie was the result of two recording sessions. Louis Prima recorded first, with the intent that Baloo—played in his recording by Butera—would simply repeat what Louie scatted, but Phil Harris decided not to imitate Prima's recording and made up his own. The song was released the same date as the motion picture itself.
The Jungle Book 2, released in 2003, featured the band Smash Mouth playing the song during the end credits of the film; the song also appeared on the film's soundtrack. In the Australian version, Nikki Webster covers the song, which is also featured on her Best of album.
The 2005 album En Vivo by Gabriel Ríos contains a cover of the song.
"I Wan'na Be like You" was covered by British recording artist Robbie Williams featuring British recording artist Olly Murs for his tenth studio album Swings Both Ways (2013). Production of their rendition was handled by Guy Chambers. However, in the liner notes Robbie Williams incorrectly attributes the original to Phil Harris, and says how much he admires Harris (p. 4 of notes in Deluxe Edition).
In 2009, "I Wanna Be like You" was used in a British anti-smoking public information film. It showed children copying everything their parents did (for example, boys putting shaving cream on their faces, girls dressing up in their mothers' best clothes and both genders washing the car), and "I Wanna Be like You" is playing throughout the advertisement, but it stops when a girl puts a crayon to her mouth in imitation of her mother smoking. It stops with the voice-over saying, "If you smoke, your children are more likely to."
The Robbie Williams/Olly Murs collaborative cover appears in season 3, episode 9 of the TV drama Stella.
In 2015, "I Wanna Be like You" was featured in season 1, episode 7 of the TV drama Aquarius.