WARNING: The Easter Egg that connects Futurama and Disenchantment appears in season 1, episode 10 of the latter series, but this article contains no actual plot spoilers for the finale.
Disenchantment appears to exist in the same universe as Futurama, as revealed by a very specific time travel Easter Egg. The Netflix show from animation legend Matt Groening takes his stylings from his previous shows The Simpsons and Futurama and transplants it to the fantasy genre. Overall, the story of Princess Bean, demon Luci and elf Elfo hews closer to Futurama, and it turns out to in more than just tone.
Groening's shows always exist in their own, uniquely-surreal twists on popular genres, but do have some sense of connectivity: The Simpsons was a show in Futurama's world, with Bart merchandise making an appearance early on (the pair later did a straight crossover suggesting they co-existed in the same continuity, although as that was from a later season of The Simpsons is readily discounted). Disenchantment takes place in Dreamland, ostensibly a high fantasy Dark Age realm: its world is an abstract approximation, with no real-world parallels (unlike, say, Futurama's New New York). However, an Easter Egg still connects the shows.
Related: Disenchantment Cast Guide
In Disenchantment season 1, episode 10 "Dreamland Falls", Luci shows King Zog a rewind of events using a magic ball. This goes through recent events in Dreamland, but in between the images of Bean, Zog et al there's one flash of Fry, Bender and Professor Farnsworth from Futurama in a spacecraft.
That craft is actually a time machine made by the Professor that formed the focal point of Futurama season 6 episode "The Late Philip J. Fry". The episode sees Farnsworth, Fry and Bender traveled forwards (and "only forwards") far, far into the future, leaving everyone they know and love behind. In the climax, they go to the end of the universe and beyond, discovering time is cyclical: they loop around through all of known history back to their starting point.
The implication of the flash is that the trio flashed through Dreamland on their way back to the present, putting Disenchantment at some point in Futurama's past. This would mean Disenchantment is in the second (or third - they end up overshooting and going all the way around again) version of the Futurama universe, although as they're all identical that doesn't matter much. Of course, this is just a quick Easter Egg it needn't mean anything major plot-wise; Disenchantment season 1 sets up more than enough storylines for the future. Besides, Futurama is a network show not owned by Netflix, making an actual crossover a la "Simpsorama" unlikely.
That said, this will surely do a lot to fuel a simmering fan theory that Disenchantment is set in the Dark Ages at all but is instead the medieval civilization seen outside the Applied Cryogenics window in the 1000 years Fry was frozen, later destroyed by aliens chasing a time-traveling Bender (see: Bender's Big Score). In the first season of Disenchantment, there's no real evidence to suggest that, so at the moment fans will have to make do with this brief crossover.