Merseyrail services will run into the early hours after the final and services will also run until after midnight on the night of the “Big Eurovision Welcome” on 7 May.
Liverpool City Region buses will also continue on key routes until the early hours following the events on 7 and 13 May.
Mersey Ferries will also operate late night services on 7 and 13 May.
Mr Rotheram said a “world class spectacular” deserved “world class transport”.
“The chance to host a global spectacle like the Eurovision Song Contest is an opportunity that doesn’t come around very often – especially for a city in the UK – that’s why so many others tried but were unsuccessful in bidding to host it,” he said.
“By organising these additional late-night services in our region, we’re ensuring that Eurovision fans and locals will get the service they deserve and won’t have to cut the party short”
Ukraine won the Eurovision contest in 2022, but it was deemed too dangerous to stage the event in the winning country this year following the Russian invasion.
It will be the first Eurovision Song Contest to be held in the UK for 25 years.
The competition is made up of two semi-finals and the grand final – all of which will be broadcast live.
This year’s semi-finals will take place on 9 May and 11 May, with ten countries from each show going through to the final.