The 30-second promotional clip features Styles, with his hair in a quiff to match Grimshaw's, waking him up with a cymbal crash and declaring: "Are you gonna get out of bed then, or what?"
Professor Green is seen hiding in the DJ's wardrobe as he decides what to wear, while Rita Ora is shown making toast for Grimshaw as he dashes out of his house to work.
Wiley and Grimshaw's Radio 1 colleague Sara Cox also appear in the video.
Grimshaw will make his debut as Radio 1's breakfast show host next Monday (September 24) and his breakfast show will feature around twice as much music as that of his predecessor Chris Moyles.
The Radio 1 Breakfast Show with Nick Grimshaw will also reportedly drop the sung jingles featured by earlier breakfast show hosts including Moyles.
Photo gallery - BBC Radio 1 breakfast show hosts through the years: