The charges, relating to an alleged Civic public fight earlier this year, were formally dismissed after the explosive revelation that a senior police officer overseeing their arrest had given "false evidence".
The two cousins spoke to media outside the ACT Magistrates Court on what was expected to be the third day of their joint hearing.
Mr Mitchell, 26, said his experience of Canberra, where he was arrested in February, had been "traumatic" and he described the criminal case against him as a "massive hit on the community".
"I hope everyone knows and understands the seriousness of what's gone on," Mr Mitchell said.
"Through the last 10 months, it's been really hard for myself. Not only myself but my family and what they've had to read and endure."
On Tuesday, Sergeant David Power admitted he had mistakenly seen Mr Wighton, 30, with "clenched fists", looking angry and in a "push and shove" with another man, causing him to kick the former Canberra Raider out of Fiction nightclub in February.
"You tried to have this man, Mr Wighton, and his mate, Mr Mitchell, convicted of criminal offences when you knew there was poison at the root of this case," barrister Steven Boland said during a heated exchange with Sergeant Power.
"You've invented a whole scenario that didn't happen."
Addressing media on Wednesday, Mr Wighton thanked Canberra Raiders CEO Don Furner.
"The club's been a huge support, they backed me the whole way through. It means the world to me. I spent so long with this club and in this town and to have your support is massive," Mr Wighton said.
"It was a long 12 months. There was a couple of big mistakes made and we've come to this result. And we'll leave it there."
The NRL players were arrested in the early hours of February 5, when celebrating Mr Wighton's 30th birthday, and charged with fighting in a public place.
Mr Mitchell was also charged with affray and resisting a public official, while Mr Wighton was charged with failing to comply with an exclusion notice.
On Wednesday, prosecutor Sam Bargwanna told the court he was offering no further evidence in relation to the charges and Magistrate Jane Campbell dismissed them.
Sergeant Power made the controversial admission at the centre of this week's hearing after police and nightclub footage of Mr Wighton was played from multiple angles, contradicting the officer's evidence.
"Sorry Jack, if that's what happened, mate. I thought I saw something different," the sergeant directly said to Mr Wighton in court on Tuesday.
"What I saw appears to have not happened. It appears my memory has failed me."
Mr Boland described the key evidence given by the officer as "total and utter fantasy".
"That you dreamt up to justify everything that happened from the moment you kicked this man, and functionally the rest of the 30th birthday, out of the club," the barrister said on Tuesday.
Mr Mitchell indicated he would be making a further statement in the coming days.
The magistrate also made an order for police to pay Mr Wighton and Mr Mitchell's legal costs.
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