Its senate voted 19 to 8 in favour of the move despite concerns that it would be seen to be favouring one religion.
The constitution says "no preference shall ever be given, by law, to any religious establishment or mode of worship".
Opponents also argued the Bible would be trivialised by being placed alongside other state symbols like the official tree, rock or amphibian.
The move comes after the sniper gun was made the official state rifle.
The bill is now being sent to the state's governor Bill Haslam who is yet to confirm whether he will approve or veto the idea.