Ronaldo, who won after the 2013-14 season, joined Barcelona star Lionel Messi as the second player to win the award twice.
ESPN will televise the European Championship in 2020 for the fourth straight time.
"Cristiano Ronaldo didn't help in any way by doing that in the final few minutes of the Euros final," Mourinho said of Ronaldo's sideline behaviour.
European football's governing body whittled a shortlist of 10 down to Real Madrid duo Bale and Ronaldo and Atletico Madrid star Griezmann.
Dallas Mavericks superstar Dirk Nowitzki brought the house down with a superb impression of Simone Zaza's infamous penalty from Euro 2016.
Leo Messi is among the 10 players who have made UEFA's shortlist for the Goal of the Season award, covering European club competitions and Euro 2016.