The clip, released on Tuesday, features "The Voice" coaches and real-life couple singing to each other and snuggling on a couch.
Shelton and Stefani have a date at a resturant and drive around happily in a car.
Shelton also dons a tie and jacket with Stefani wearing a sparkling dress for an onstage performance.
"I don't wanna live without you/ I don't wanna even breathe/ I don't wanna dream about you/ I wanna wake up with you next to me/ I don't wanna go down any other road now/ I don't wanna love nobody but you/ Lookin' in your eyes now, if I had to die now/ I don't wanna love nobody but you," the duo sing together during the chorus.
"Nobody But You" appears on Shelton's 2019 compilation album "Fully Loaded: God's Country."
Shelton and Stefani, who confirmed their relationship in November 2015, will be performing together at the Grammy Awards on Sunday.
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