I got slightly confused by the previous comments, so here's what I learned about this quest:
(tell me if something is unclear, and I will try to simplify it more)
--> This quest is NOT linked to the legendary quest.
--> You need to gather & turn in 4 items before this quest appears and YES you can gather all 4 before turning any of them in. The items are collected from 4 areas (Gorgrond, Frostfire Ridge, Nagrand & Talador)
--> It seems like only lvl 100+ can complete this according to comments, but I haven't personally tried a lower lvl.
--> The items are shown as quests on the minimap and there will be a big coloured orb above the items (purple-ish, yellow-ish)
--> The quests will be turned in at Zooti Fizzlefury in Talador at Khadgar's Tower and he will THEN give you this quest which will summon Archmage Image (follow Zooti to the summon). The Image will give you the quest The Staff of Archmage Vargoth which gives you the follower called Image of Archmage Vargoth.
--> The 4 items:
Mysterious Ring : The ring is found in Gorgrond (39.7, 39.9), south from Skysea Point. Fly there and travel a little south until you come to the enemies. Look to the right and you will see a top, go there and the ring will be in a crater (look for the quest on the minimap)
Mysterious Boots : The boots are found in Frostfire Ridge (68, 19). Enter Magnarok (located north eastern corner) and travel north, just follow the mountain without climbing. There will be a path with a 100 elite guarding it, run through that so you will still follow the mountain's feet. You should see the item very soon (if you look at the map, the item will be between the texts "Magnarok" and "Colossal's Fall" but to the north.
Mysterious Hat : The hat is in Talador (45.3, 37), in Shattrath City. If you enter the City from the eastern road, follow the road west down 2 stairways and the hat will be to the left at the square (it lays between a wide stairs and a double stairs. If you look at the map, it's northeast of the blue "flower" and southeast from the purple circle. This is the lvl 100 area, NOT elite 100s.
Mysterious Staff : The staff is found in Nagrand (46.4, 16), eastern side of Broken Precipice. Simply follow the road that goes north next to Broken Precipice, into the mushroom area. You will see the quest on the minimap when the road ends (north from the end). I received a debuff that hurt when I entered this shroom area, so dont go afk in case you get it too ;)
If you dont know if you've completed any of the 4 items, type the following code into your chat window (credit to res1233). True means completed, false means not completed.
/run local itemArray={"Ring: ","Boots: ","Hat: ","Staff: "} for i=34463, 34466 do print(itemArray[i%34462]..tostring(IsQuestFlaggedCompleted(i))) end