The 36-year-old has spent nine seasons in England spending six seasons with Essex before moving to Lancashire.
"Im glad that its happened quickly and with no problems. I can now start the New Year and new season as an English player and hopefully in the long run benefit Lancashire," said Law.
Law has scored 23,000 first-class runs, with 68 centuries and at an average of 51.21.
He played just one Test for Australia but has also appeared in 54 one-day internationals.