The agreement will result in train operator Keolis Downer Adelaide and tram operator Torrens Connect handing back operational functions by January 2025 and July 2025 respectively.
Premier Peter Malinauskas says unnecessary privatisation of a state asset has been consigned to history.
"Labor went to last year's election with a clear policy to end the former Marshall Liberal government's failed privatisation of train and tram services," he said in a statement on Sunday.
"We are delivering on that election commitment with a deal to return train and tram operations to public ownership."
Train customer service and security management functions will be returned to government control by June 2027 and Keolis Downer Adelaide will continue to provide fleet and infrastructure maintenance services under contract until 2035.
Mr Malinauskas said passengers would not be impacted during the transition period and Adelaide Metro operations will continue to run as normal.
About $30 million will be invested over the next two years as the government prepares to take operational control of the train fleet, along with about $3 million in transitional arrangements for the tram services.
Under the tram deal, Torrens Connect will return operations, including drivers, operations control, customer service, network and timetable planning to government hands by August 2025.
The former Marshall government privatised tram services in 2020 and train services in 2021 under separate contracts, each for an initial eight-year term with an option to extend to 10 and 12 years, respectively.
No penalty fee will be paid to the operators for ending those contracts.
The Rail, Tram and Bus Union said the agreement was a huge win for local commuters and transport workers.
"This announcement means that taxpayers' money that is budgeted for public transport will actually go into public transport - without a private company clipping the ticket on the way through," SA branch secretary Darren Phillips said.
"And it means that transport workers will be able to negotiate with an employer that cares about South Australians, and cares about more than just maximising profits."
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