The project is focused on the core Valley lines, which connect Cardiff with Aberdare, Merthyr Tydfil, Rhymney, Coryton, and Treherbert.
While the Metro map resembles the London Underground, most of the network will remain above ground, except for small sections such as the tunnel between Cardiff and Caerphilly.
The first phase of the Metro is set to be completed by early 2026.
By then, residents in Aberdare, Merthyr Tydfil, and Treherbert will have access to four trains per hour to Cardiff, with Pontypridd benefiting from a train every three minutes.
Built by Stadler, the new Class 756 Fast Light Intercity and Regional Trains (FLIRTs) will run on newly installed overhead electric wires carrying 25,000 volts.
On tracks without electrification, they can switch seamlessly to diesel or battery power, making them versatile and environmentally friendly.
Ken Skates, Wales' Cabinet Secretary for Transport, said: "These state-of-the-art electric trains will make passengers' journeys more comfortable and encourage more people to use the train for their travel needs."
Emil Hansen, Commercial Project Manager for Stadler, added: "We are thrilled to see the UK's first FLIRT tri-mode enter passenger service in Wales.
"These rail vehicles represent a significant leap forward in efforts to drive decarbonization."
The project, which has been partly funded by the European Regional Development Fund through the Welsh Government, aims to create a greener, more efficient transport network while reducing carbon emissions.
Price said: "We've been modernising and electrifying the railway lines for the last three years, and this signifies the next phase of the South Wales Metro."