The governor extended the invitation a day after TDP Legislature Party (TDPLP) elected Naidu as its leader.
Earlier in the day, a delegation of TDP leaders met the governor and informed him about Naidu's elections as the TDPLP leader.
Naidu, who was chief minister of undivided Andra Pradesh 1995-2004, was unanimously elected as the leader at the TDPLP meeting held at Tirupati Wednesday night.
The 64-year-old will take oath as the chief minister at Mangalgiri in Guntur district on June 8. He will be the first chief minister of Andhra Pradesh after Telangana state was carved out.
The TDP bagged 102 seats in 175-member Andhra Pradesh assembly in the recent elections.