Wowhead posted a list of Artifact Traits and Legion Legendaries that will be returning in BfA. For ease of reading or for those that don't visit Wowhead, I'll be posting the list here
Demon Hunter
Havoc
The Legendary Anger of the Half-Giants became the new talent Insatiable Hunger (Demon's Bite generates up to 10 additional fury).
Vengeance
The artifact trait Fueled by Pain was turned into the talent Gluttony (Consuming a Soul Fragment has a chance to activate Metamorphosis for 5 sec).
The artifact trait Fiery Demise was buffed and turned into the talent Charred Flesh (Fiery Brand increases the Fire damage your abilities deal to the target by 20%).
Druid
Restoration
The main artifact ability Essence of G'Hanir had its effects baked into the Flourish talent (Extends the duration of all of your heal over time effects on friendly targets within 60 yards by 8 sec, and increases the rate of your heal over time effects by 100% for 8 sec), which had its cooldown increased to 1m30 to accommodate that buff.
Hunter
Beast Mastery
The legendary Qa'pla, Eredun War Order likely inspired the new effect on Cobra Shot (A quick shot causing [(35.36% of Attack Power) * ((min(Level - 1, 19) * 12+112) /340)] Physical damage. Reduces the cooldown of Kill Command by 1 sec.
The artifact trait Healing Shell was buffed, has its utility available via Natural Mending (Exhilaration heals you for an additional 20% of your maximum health over 10 sec), with Exhilaration instead of Aspect of the Turtle as a trigger.
Mage
Arcane
The artifact trait Rule of Threes (You have a 33.3% chance to fire 3 additional Arcane Missiles) likely inspired the new talent Mana Adept (While you are above 80% mana, Arcane Missiles fires 2 additional missiles).
Fire
The main artifact ability Phoenix's Flames became the new talent Phoenix Flames (Hurls a Phoenix that deals (100% of Spell Power) Fire damage to the target and splashes (31.25% of Spell Power) Fire damage to other nearby enemies. This damage is always a critical strike).
Monk
Windwalker
The main artifact ability Strike of the Windlord (Strikes with both Fists of the Heavens at all enemies in front of you, dealing (933%+933%) damage and reducing movement speed by 50% for 6 sec) likely inspired the new talent Fist of the White Tiger (Strike your target with the technique of the White Tiger, dealing [(112.5% of Attack poewr) + (112.5% of Attack poewr)%] Physical damage to your taget while generating 3 Chi).
Paladin
Retribution
The main artifact ability Wake of Ashes became the new talent Wake of Ashes (Lash out at your enemies, dealing (163.8% of Attack power)% Radiant damage to all enemies within 12 yards in front of you and reducing their movement speed by 50% for 5 sec. Demon and Undead enmies are also stunned for 5 sec.
Priest
Holy
The artifact trait Cosmic Ripple (When Holy Word: Serenity or Holy Word: Sanctify finish their cooldown, you emit a burst of light that heals up to 5 injured targets for (30% of Spell power).
Shadow
The main artifact ability Void Torrent became the new talent Void Torrent (Channel a torrent of void energy into the target, dealing (300% of Spell power) Shadow damage over 4 sec. Insanity does not drain during this channel.
The legendary ring The Twins' Painful Touch (Mind Flay cast after entering Voidform spreads Shadow Word: Pain and Vampiric Touch to 3 enemies within 10 yards of your target) likely inspired the new talent Dark Void (Void Eruption applies Shadow Word: Pain to all targets hit).
The multiple Mind Blast charges given by the legendary Mangaza's Madness are now given by the talent Shadow Word: Void (Blasts the target with a word of void for (175% of Spell power) Shadow damage), which also increases its damage.
Rogue
Assassination
The effect from the class legendary Mantle of the Master Assassin is now the Assassination talent Master Assassin (While Stealth is active and for 3 sec after breaking Stealth, your critical strike chance is increased by 50%).
The artifact trait Bag of Tricks became the new talent Poison Bomb (Envenom and Rupture have a 4% chance per combo point spent to smash a vial of poison at the target's location, creating a pool of acidic death that deals [(9.828% of Attack power) * 6] Nature damage over 3 sec to all enemies within it.
Outlaw
The artifact trait Loaded Dice (Activating Adrenaline Rush causes your next Roll the Bones to grant at least two matches) is now a talent.
Shaman
Elemental
The main artifact ability Stormkeeper became the new talent Stormkeeper (Charge yourself within lightning, causing your next 2 Lightning Bolts or Chain Lightnings to be instant cast and trigger an Elemental Overload on every target).
The artifact trait Volcanic Inferno (Lava Burst has a chance to open a volcanic fissure under your target, dealing (6 * (15% of Spell power)) Fire damage over 6 sec to all enemies within 3 yards of the target) likely inspired the new talent Volcanic Rage (Erupt a volcano under your target's location, causing (250% of Spell power) Fire damage to all enemies within 8 yards and applying Flame Shock to all targets hit for 12.0 sec).
Enhancement
The artifact trait Doom Wolves became the new talent Elemental Spirits (Your Feral Spirits will be imbued with Fire, Frost, or Lightning, enhancing your abilities).
Warlock
Affliction
The effects from the legendary Hood of Eternal Disdain (Agony deals its full damage 10% faster) likely inspired the new talent Creeping Death (Your Agony, Corruption, and Unstable Affliction deal their full damage 15% faster).
Warrior
Arms
The main artifact ability Warbreaker became the new talent Warbreaker (Smash the ground and shatter the armor of all enemies within 8 yards, dealing (155% of Attack power) Physical damage and increasing damage you deal to them by 30% for 10 sec).
The legendary ring Ayala's Stone Heart had its effects transfered into the talent Sudden Death (Your damaging melee abilities have a chance to make your next Execute cost no Rage, be usable on any target regardless of their health, and deal damage as if you spent 40 Rage).