Their confession came after the New Zealand Herald today reported the pair had gone out drinking and been questioned by Chennai police after sparking a riot while trying to give money to the poor.
Once police realised the pair were New Zealand cricketers they were put into a taxi and sent back to their hotel.
New Zealand Cricket (NZC) had charged the players with serious misconduct but did not make public the incident.
"... the incident was dealt with thoroughly and appropriately at the time," NZC chief executive Justin Vaughan said today.
Both players had accepted they had acted inappropriately and breached security protocols on the tour, he said.
Vaughan did not reveal any details regarding punishment meted out to the players.
"It was a confidential process, and New Zealand Cricket considers the matter closed." Broom and Redmond said they put their hands up today so no other player was unfairly associated with the misconduct.
Redmond said they had not informed team management they would be leaving the team's hotel.
"Unfortunately when we decided to leave the night spot we were picked up by police following another poor decision to hand out money to people living on the street, whereupon a crowd developed," Redmond said.
"The police initially took us back to the station and then arranged for a taxi to take us back to the hotel," he added.
Broom said the pair deeply regretted the incident and had apologised to NZC.
"We also wish to apologise to other stakeholders in the game including the fans for our inappropriate behaviour while on tour," Redmond said.
New Zealand Cricket Players Association executive manager Heath Mills said it was important to note no crime had been committed nor were charges laid against the players.
"The players fully accept that they should not have left the hotel, and also showed poor judgment in heading to a night spot and drinking, given preparations required for upcoming fixtures and the security position the team was in."
