The news will come as a bombshell to Assange's friends and enemies since he was widely understood to have led a near-monastic life since entering the embassy in 2012.
At the time, Assange, 48, was also wanted in Sweden where he was accused of rape. He has always denied the sex allegations, which have now been dropped.
The boys' mother is 37-year-old South African-born lawyer Stella Morris, who fell in love with the controversial WikiLeaks founder five years ago while visiting him to work on a legal bid to halt the extraditions.
The couple have been engaged since 2017.