Dousing the coach with a bucket of Gatorade seems to have been around from the beginning of time, but it's actually only been around since the early-mid 80's. The Chicago Bears are believed to be the originators when they soaked head coach Mike Ditka after winning the NFL Central title in 1984.
The Giants get the credit for popularizing it, however. First by DT Jim Burt in 1985 and then LB Harry Carson took the reins in the Giants' Super Bowl run the next season. (Mental Floss). Parcells got 17 Gatorade showers during the 1986 season, including the well-dcoumented one at the end of Super Bowl XXI.
For a history of Gatorade showers, read Sam Borden's NY Times piece from 2012.