The 21-year-old, who was taking part in the Olympics for the first time, was arrested on Thursday on suspicion of criminal damage.
Police were called to Egham High Street in Surrey at about 1.40am on Thursday and Joshua was taken into custody.
The rower was staying with other Australian rowers at Eton Dorney Centre in Lake End Road in Dorney which is near to the Olympic venue. It is a former vicarage owned by Eton College.
Police said the rower has admitted full responsibility for the damage caused.
Officers said they spoke to the owners of both damaged properties and, following an offer of reparations to cover the costs of repairs by Joshua, the victims are satisfied that the matter can be dealt with without the need for criminal charges.
A spokesman said that Joshua had shown remorse and a willingness to make amends for the damage caused.
He has been released by police without charge.
Chief Superintendent Gavin Stephens said: "Mr Booth is extremely fortunate that the victims in this case have accepted the offer of reparation, as there are no excuses for criminal damage, whatever the circumstances."
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