If you need any assistance installing through Steam our support page has a step-by-step. As was mentioned, the Steam client likely will not recognize the game without a new installation.
This only works for a game purchased through Steam. If you purchased the game through our website or a retailer you don't need to move any files, just to add it as a non-Steam game. The game cannot be registered as a full Steam game if it isn't purchased through their store.