A cheeky Victorian premier has teased his New South Wales counterpart after Melbourne fought off Sydney to secure the Formula One Grand Prix until 2023.

In a video posted on Facebook, Premier Daniel Andrews held a copy of the Daily Telegraph's front page where New South Wales Premier Mike Baird made a bid to steal the race from Melbourne.

"I'm sorry Mike but the Australian Formula One Grand Prix is here to stay exactly where it belongs, in the great city of Melbourne," Mr Andrews said on Saturday night.

"The good news is that you and tens of thousands of others from New South Wales and right across Australia and indeed right across the world are more than welcome to come to Melbourne to be part of the great race.

"In fact I'll even shout you a ticket."

The video was posted with an announcement that Melbourne would host the race at least until 2023 with the hashtags #sorrynotsorry and #bestofeverything.

Mr Baird announced during the New South Wales election campaign in March he would work on bringing the grand prix to Sydney if elected.

The New South Wales plan included racing the F1 cars across the Sydney Harbour Bridge.

The two premiers have used social media to poke fun at each other in the past.

When Victoria announced its new branding "Best of Everything" last month, Mr Baird was quick to add a disclaimer on Twitter saying: "offer excludes harbour, infrastructure and sunshine."

To which Mr Andrews replied: "You're just grumpy because you haven't had a decent coffee since you were last in Melbourne!"

AAP /ABC