One could argue that the existence of Artifact Weapons kind of takes the place of Legendaries. From Vanilla through Cataclysm, Legendaries were always weapons, often involving long and complex quest chains (though in BC, they were simply somewhat rarer drops off of bosses very few players would ever even fight.) Mists certainly kept the long and complex quest chain, bumping it up to an expansion-long one (a model that Warlords continued, albeit in a more simplified, somewhat more raid-oriented manner,) but in order to accommodate all classes and specs, they were made universally-equipped items, a cloak and a ring.
Legendaries will work far, far differently in Legion. Essentially the expansion-long goal of super-powering some piece of gear will be all about the artifacts, which also have the added advantage of each having a unique backstory behind them.
There will still be legendary items, but it looks like they'll actually be working a lot more like Diablo-style legendaries. In Diablo III (the only one I've played, so this might be the case in earlier games as well,) legendaries are, like pretty much all gear, generally random drops (some are made via blacksmith plans, but of course those recipes are also random drops.) What makes Legendaries interesting is that most of them have some kind of unique effect. For example, there's a pair of boots that constantly does mild fire damage to any enemy standing near you.
The Legendaries in Legion will be more like this - they'll be rare drops that I believe can drop just about anywhere, and they'll have unusual effects. Right now the ones that have been datamined sometimes have flavor text, but the effects are not there yet.
What we do know, however, is that a lot of these legendaries will be for specific classes and specs, meaning that they will be able to interact with our abilities in interesting ways. Things like these or set bonuses (and I believe some of the random world drops will be class-sets) make gearing a more interesting game - there could be an effect that's might be more important than just getting a bit higher item level, so you have to decide what's worth keeping and what you move on from.
Legendary chains can be fun, but honestly I think the class-specific stuff we're getting, apparently all expansion long, along with our artifact weapons, will give us plenty of interesting plot threads to work through. There were some good moments in the Warlords legendary chain, but let's be honest - it was mostly just grinding bosses for quest items. I'm curious to see how this experiment works out.