The London 2012 Australian team members were to leave the Olympic village at the completion of swimming events as the result of a photo posted on Facebook which showed the pair holding firearms while training in the US.
Australian chef de mission Nick Green, who imposed the punishment, said earlier this week that the pair would still be sent home on August 4 as originally planned.
But in a statement issued on Saturday an Australian Olympic Committee spokesman said the team executive had agreed to a change in plans to allow them to leave with their families.
"They have surrendered their accreditation and left the Olympic Village," the statement said.
"The AOC team executive has agreed to this change in plans on the basis that Monk and D'Arcy do not remain in London or return to London during the period of the London Olympic Games.
"They have given an undertaking to adhere to the earlier sanction and not engage in social media activity during the Games' period."
The statement said the swimmers were now in the care of their families and it is believed the pair have already left London for Croatia to join family and friends on holiday.
Their travel back to Australia would be at their own cost, the statement said.
The pair had been due to leave London on Saturday night along with disgraced Australian rower Josh Booth who this week was ejected from the Olympic camp for a drunken rampage during which he damaged two shopfront windows.
Booth is now due to leave on Sunday night and return to Melbourne on Tuesday morning.