NZR launched an independent investigation into allegations Mo'unga spat beer on people at a Cape Town bar, while Bridge was accused of making homophobic slurs towards patrons in a fast-food restaurant in the city later in the week.
"NZR's investigation has found that the allegations against George Bridge were not upheld," NZR's Head of Rugby Nigel Cass said in a statement on Monday.
"With regard to Richie Mo'unga, the NZR investigation found that the allegations also could not be substantiated.
"Given the seriousness of these allegations, and the potential consequences, we needed to be confident that what was alleged, actually took place, and we weren't."
Cass, however, said that Mo'unga's response to the female complainant was "not consistent with NZR's values".
"He (Mo'unga) has acknowledged this and subsequently apologised," Cass said.
"We feel that he has learned some valuable lessons and we are satisfied that he will not put himself in the same position again in future."
NZR added they had asked the Crusaders to "urgently" review their team protocols around players' after match socialising.
The governing body said they considered the investigation to be closed, which should free both players for selection for the Super Rugby final against the Jaguares on Saturday in Christchurch.
The Crusaders are seeking their third successive title under coach Scott Robertson, and 10th overall, in Saturday's match against the Argentine side.
Robertson told reporters in Christchurch there were some concerns over the fitness of first-choice lock Scott Barrett (finger) and inside centre Ryan Crotty (thumb), who were injured in the 30-26 win over the Wellington Hurricanes on Saturday.
The physical clashes in the semi-final reached test level intensity at times and Robertson said they would take a lighter approach this week to prepare for the onslaught from what is essentially the Argentine national team.
"We will train light, there's no doubt," Robertson said.
"We will get through so we are in the best possible nick we can be, and more importantly - mental condition - so we have a great night on Saturday."
(Writing by Greg Stutchbury; Editing by Sudipto Ganguly)
