When was the whole world known?
Comparing on just how detailed you needed it to be, it would be around the 1700s when Australia is discovered enough so that Northern Queensland and the Northern Territory would be on the map. For example here is a map of the world from 1708.
http://www.worldmapsonline.com/historicalmaps/kr-1708-world.htm
As you can see on this map you would recognise any modern map as the same just with a little more information on the east coast of Australia.
Roger II of Sicily commissioned the Tabula Rogeriana, completed in 1154 and drawn by Muhammed al-Idrisi. It somewhat accurately mapped out the area from Spain to China, south to Africa. It was compiled through interviewing as many merchants/travelers passing through Salerno as possible and is pretty dead on if you take a look at it.
Edit: Just realized you said world map, but hopefully this still helps you out.
I'd say just after WW1. An interesting article on Sykes-Picot:
Are you talking about in terms of geography or in terms of political boundaries?