According to Law 3 of FIFA Laws of the game.
Any of the other players may change places with the goalkeeper, provided that:
- The referee is informed before the change is made
- The change is made during a stoppage in the match.
I could not find mention of the changing of the jersey, but as per custom, usually the goalie in indicated by wearing a different color.
According to Law 4, the goal keeper must wear colours that distinguish him from other players, the referee and the assistant referees.