Dua Lipa's eponymous debut release and afrobeats rapper J Hus's Common Sense are also up for the prestigious prize which was won posthumously by David Bowie at last year's ceremony.
Sheeran received a third nomination in best British video, again for "Shape of You", and is joined in the category by Dua, Clean Bandit and Zara Larrson, Calvin Harris, Anne Marie, Zayn Malik and Taylor Swift, Little Mix and Jonas Blue.
Foo Fighters - who will perform at the 38th Brits next month - are nominated for best worldwide group alongside fellow United States acts Haim, The Killers and LCD Soundsystem, as well as Canadian group Arcade Fire.
Former One Direction bandmates Liam Payne and Harry Styles will also compete against one another in the category, for their singles "Strip That Down" and "Sign of the Times" respectively.
Taylor Swift, Lorde, Bjork, Pink and Alicia Keys are all nominated for best worldwide female while actor Donald Glover's musical alter-ego, Childish Gambino, earns a nod in the best global male category.
Ed Sheeran, pictured here performing at Glastonbury Festival, has been nominated for four Brit Awards.
The 2018 Brit Awards will take place 21 February at the O2 Arena in London, and the categories video of the year and breakthrough act are open to voting at the official website.
East London rapper J Hus and platinum-selling songwriter Rag'n'Bone Man have three nominations apiece, including for best album, while Stormzy's Gang Signs and Prayer is also nominated.