Appearing at the Melbourne Magistrates' Court on Saturday, Rogers was granted bail under the condition that he must report to police daily, abide by a curfew, undertake drug screenings, and a court program to help with substance abuse.
Rogers gained instant fame when video posted on social media showed him using a metal shopping cart to try and stop a stabbing rampage in central Melbourne by Hassan Khalif Shire Ali, who killed one man and wounded two others before being fatally shot by police.
He was remanded to appear in Melbourne Magistrate's Court today.
Police confirmed on Saturday a man had been charged with two counts of burglary, two of theft and committing an indictable offence while on bail.
Police are expected to oppose that application.
An online fundraising campaign for Mr Rogers has raised more than A$140,000 ($103,000; £80.000).
Netanyahu battles to save weakened ruling coalition
But Yisrael Hayom said Bennett was key to efforts to avoid an early election and could yet prove Netanyahu's political salvation. However, opinion polls cited by Reuters show that Likud would likely remain the dominant party after a parliamentary election.
Donna Stolzenberg, director of the National Homeless Collective charity, which set up the online fundraiser for Rogers, said he was keen to do the right thing and hand himself in to police.
Mr Rogers was called in by police for questioning on Friday.
She said the more than $145,000 raised for Mr Rogers would go towards support and accommodation for the homeless man.
"I'm not saying what I did wasn't good, but you know, you've got the police, you've got the Army, you've got the ambulance - you've got better heroes than me", he said.
The fund's website says it will be held in a trust account to ensure he "is well taken care of and guided financially as he moves forward".
Rogers also faced charges over an offence in October where he was accused of following someone into a St Kilda Road apartment building and stealing a $2000 bicycle from a storage cage.