I'm looking for canon for what the process was that chose Hogwarts to host the Triwizard Tournament after its reinstatement in GoF. Anything JKR said, preferably.
According to Goblet of Fire, the tournament host rotates between the three major Wizarding schools: Beauxbatons Academy of Magic, Durmstrang Institute, and Hogwarts School of Witchcraft and Wizardry.
These three host schools were chosen because, as the primary source of Wizarding education in Europe, a friendly rivalry had built up between them. (No mention is made why the Wizarding Schools from other continents didn't participate, though obviously it would no longer be the TriWizard Tournament.)
When the Tournament was revived during the 1994/95 school year, it was Hogwarts turn to host it, so they hosted it.