Premier Daniel Andrews announced on Monday that Melbourne Arena would become John Cain Arena as a tribute to the state's 41st premier, who died aged 88 on December 23.

Mr Cain is credited with moving the Australian Open from Kooyong to the Melbourne Park precinct, then known as the National Tennis Centre, ensuring the Grand Slam tournament remained in the state.

"John Cain made an enormous contribution to Victorian life and it's particularly appropriate that we honour his legacy at Melbourne Park," Mr Andrews said in a statement.

"People will see his name and know the story of a man who made our state a better place."

Mr Andrews said the renaming of the arena will happen in the coming months, with the move endorsed by Tennis Australia, which has agreed to relinquish naming rights.

The announcement comes ahead of a state memorial service for the longest-serving Labor premier, which will be held at St Paul's Cathedral at 11am on Monday.

Doors open at 10am, with members of the public encouraged to attend.

Mr Cain's family has asked people to consider making a donation to the Victorian Bushfire Appeal in lieu of floral tributes.

Australian Associated Press