The humorous and action-packed trailer is the first chance for fans to see Sheen, a fussy angel, and Tennant, a loose-living demon, as the unlikely biblical duo who must join forces to stop Armageddon.
The clip shows Sam Taylor Buck as an unknowing young Antichrist, whose presence could bring on the end of days, and the arrival of the Four Horsemen of the Apocalypse, who appear on motorbikes.
The first-look trailer, backed by Queen and David Bowie’s Under Pressure, also shows glimpses of cast members including Jon Hamm, Nick Offerman and Jack Whitehall.
Mad Men star Hamm plays Archangel Gabriel, the leader of the forces of Heaven, while Parks and Recreation star Offerman is a US ambassador.
Comedian Whitehall, seen caught up in a surprising tornado in England in the trailer, is Newton Pulsifer, who helps the angel and demon in their battle to stop the Apocalypse.
There is also a look at what appears to be Satan, played by Benedict Cumberbatch.
Good Omens - which was announced in August 2017 - is based on the novel Good Omens: The Nice And Accurate Prophecies Of Agnes Nutter, Witch, co-written by Sir Terry Pratchett and Neil Gaiman.
Its ensemble cast also includes Frances McDormand, who plays God, Miranda Richardson, Michael McKean, Anna Maxwell Martin, Josie Lawrence, Reece Shearsmith and Sir Derek Jacobi, among others.
Good Omens premieres on Amazon Prime Video on May 31.