The couple, who met on the set of the 1986 action film, are understood to have separated last month, and their split has been "amicable", a representative for the 74-year-old actor told TMZ.
According to the website, Linda, 55, has cited "irreconcilable differences" in her divorce papers, requesting spousal support and joint legal and physical custody of their 15-year-old son Chance.
She has also asked for her maiden name of Kozlowski to be restored.
There were reports that the couple were having problems when they sold their Malibu home to fellow Australian Chris Hemsworth last month.
Linda and Paul, who is worth a reported $20 million, were married in 1990 after falling in love on the Crocodile Dundee set.
This will be the film star's third divorce; he married first wife Noelene in 1958 and divorced her in 1981. The couple had five children together.
They remarried a year later but divorced for a second time in 1986 after a long and drawn out court battle.