Allmusic critic William Ruhmann praised the song: 'Recalling Dylan's bitter 1964 song "It Ain't Me Babe" (soon to be a folk-rock hit for the Turtles), Bono wrote his own opposite sentiment: "I Got You Babe." Where Dylan was lyrically complex, Bono was simple: His lyric began with the ominous youth-versus-grownups theme of "they" who set up barriers to romance, but soon gave way to a dialogue of teenage romantic platitudes. Where Dylan was musically simple, however, Bono, without fully rebuilding Spector's Wall of Sound, was more structurally ambitious, following the song's standard verse-chorus-verse-chorus-bridge-verse-chorus form with an ascending coda that built to a climax, then started building again before the fadeout, all in only a little over three minutes. Set to waltz time, the tune retained a light feel despite the sometimes busy instrumentation, led by a prominent oboe, and the alternating vocals of the two singers. If neither Bono nor Cher were interesting singers, their plodding, matter-of-fact performances gave the song a common-man appeal.' Bruce Eder highlighted the song on the "Look at Us" album.
In the United States, the song has sold more than 1 million copies in 1965 and was certified Gold by the RIAA. As of November of 2011, Billboard reported the digital sales of "I Got You Babe" to be 372,000 in the US.
In 1993, Cher did a version of her 1965 duet with her then husband Sonny Bono with the American animated characters Beavis and Butt-head. The song was the first single from The Beavis and Butt-Head Experience, a compilation comedy album released in 1993 by the Geffen Records, which is one of the fastest selling comedy albums and has officially sold 1,610,000 units and was certified 2x Platinum by the RIAA in the United States. Allmusic reviewed this song by calling it "most interesting" and added "Throughout the song, the duo decide they need a "chick who's older, who's done it a bunch of times," then proposition Cher by making fun of her ex-husband Sonny Bono". The single reached top 40 in the UK and Sweden, as well as the top ten in the Netherlands and Poland.
A funny and psychedelic video was produced which got a lot of MTV airplay. It featured Cher and Beavis and Butt-head in a virtual animated world. In the video, the animated pair refer to her former husband Bono as a dork and a wuss, to which Cher agrees. It was placed at number 5 on the "50 Greatest Funny Moments in Music" list made by Vh1 channel in 2004.
The song has been frequently covered and featured in film and television, including Sonny and Cher's own The Sonny and Cher Comedy Hour. "I Got You Babe" made a bit of a comeback when it was used repeatedly as Phil Connors' alarm clock wake-up music in the 1993 movie Groundhog Day. On re-release, the single re-charted in the UK, reaching #66.