The WikiLeaks founder entered the embassy in London in 2012 to avoid extradition to Sweden, where he was wanted in connection with sexual offences allegations.
He spent nearly seven years living in the embassy until being dramatically dragged out by police in April after Ecuador revoked his political asylum.
The 48-year-old was jailed for 50 weeks for breaching his bail conditions, just short of the one-year maximum for the offence.
He lodged an appeal against the length of his sentence and a hearing was due to take place at the Court of Appeal in London on July 23.
But Assange is no longer pursuing the appeal and a spokeswoman for the judiciary confirmed on Thursday that the planned hearing had been cancelled.
Assange entered the embassy on June 19 2012 while under intense scrutiny over the leaks of hundreds of thousands of classified US diplomatic cables on his whistle-blowing website.
The drastic move came after he exhausted all legal options in fighting extradition to Sweden over two separate allegations - one of rape and one of molestation.
Assange, claiming he was the subject of an American "witch hunt", said he was at risk of being taken to the US if he was sent to the Scandinavian nation.
His eviction from the embassy on April 11 came after a souring of relations, with Ecuador's president Lenin Moreno claiming Assange had tried to use the Knightsbridge site for spying.
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