Assange has been holed up at the diplomatic mission since 2012, when President Rafael Correa granted him asylum.
Before the election, conservative banker Guillermo Lasso had said he would evict the Australian activist, who is wanted for extradition by Sweden, within 30 days of taking office.
Ruling-party candidate Lenin Moreno, the apparent winner in yesterday's tight race, said he would allow him to stay.
On his Twitter account shortly after the results became known, Assange took a jab at Lasso's pledge.
Assange, whose relationship with Correa's government has been rocky, also appears to want to make nice with his new host.
Today, he posted two secret US diplomatic cables on Moreno that describe the politician in flattering terms.
In one from 2007, former US Ambassador Linda Jewell describes Moreno as a bridge builder will have a good sense of humour who will have a moderating influence on Correa, a firebrand leftist who closed down a US military base.
Last year, Assange found himself in an angry public dispute with his hosts, who briefly cut off his Internet access in retaliation for WikiLeaks' publishing of supposedly damaging emails targeting Hillary Clinton's presidential campaign.
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