The 61-year-old, of Westleigh Lane, Leigh, was jailed for 12 years by Judge Timothy Stead at Bolton Crown Court in July.
But his sentence was increased to 16 years after his case was referred to the Court of Appeal, in London, by the Solicitor General, Robert Buckland.
Lord Justice Davis said the original term was "unduly lenient" in light of Kirkby's catalogue of crimes and the number of victims.
Sitting with Sir David Calvert-Smith and Judge Simon Bourne-Arton QC, he added: "There were four victims and, of the counts charged, many were accepted to be specimen counts involving incidents on many occasions.
"The effect on the victims has been profound, the crown court judge was right to say this was a campaign of sexual offending.
"We think the least sentence appropriate for this case is one of 16 years."
A one-year extension to the licence period Kirkby will be under following his release from jail remains in place.