A spokesman for the Judicial Office confirmed that lawyers for the 84-year-old had lodged papers at the Court of Appeal this week.
The artist and musician was convicted of 12 indecent assaults on June 30 at Southwark Crown Court - one on an eight-year-old autograph hunter, two on girls in their early teens and a catalogue of abuse of his daughter's friend over 16 years.
The court will now consider whether to grant permission for him to continue with his appeal bid.
Harris was unmasked as a predator who was fixated with under-age girls during his trial, with jurors told how his sex abuse of his daughter's friend "haunted" her.
He was stripped of a Bafta fellowship and accolades in his native Australia and could lose his CBE.
The performer's fortune is also at risk from potential compensation claims.
Harris was jailed for five years and nine months meaning that he is due to serve just under three years for the crimes.
Earlier this week the Attorney-General's Office confirmed that the sentence would not be referred to the Court of Appeal for being unduly lenient.