The Oxford Companion to Chess gives the following information:
"Promotion dates from the earliest times ... The first original work in German (1728) stated that a promoted pawn could be exchanged only for a piece that had already been captured ... the current law of promotion is essentially the same as that used by Staunton for the first international tournament, London 1851."
Your mention of 'some other piece' should be clarified to mean, "queen, rook, knight, or bishop." You cannot get a king for that would make the game essentially impossible to win, having to checkmate two or more kings. Nor can you leave the piece a pawn, though that "at the end of the 18th century, Allgaier demonstrated that the absurdity of ..." leaving the pawn a pawn until another piece was captured.
This may be just a silly question, but, When a pawn reachs the eight square it must be exchanged for some other piece of the same colour before the move is complete. Why can't it be another King? I know a queen is choosen in most games, but another king would add new variations to the game if it were to be a option. Can anyone help me find out where or why this rule is in the game of chess.