The 932-tonne structure was transported to the west-facing freight port following a one-day journey from Cork in Ireland, where it was built.
Work will shortly begin to install the infrastructure at the port which is expected to be fully operational later this year following stringent testing.
Peel Ports said the cranes are the largest single investment made at the container terminal and will help accommodate increased demand from cargo owners, and support growth in transatlantic trade, as well as future proof the port.
The capabilities of the new cranes have already been key in securing new routes, the operator added, including a new weekly deep sea container service connecting Scotland to the Mediterranean market of Turkey.
Jim McSporran, Port Director at Peel Ports Clydeport, said: “These two structures will be transformational for the port, significantly expanding our freight capabilities here, and we’re all really excited for having them fully operational later this year.
“Once installed they will also boost efficiency and bring more opportunities for global connections and worldwide trade into Greenock, further strengthening our position as a major port for importers and exporters.”
The cranes are to be named ‘U-Crane Bolt’ after the Jamaican Olympic gold medallist Usain Bolt and ‘Craner Swift’ in tribute to Taylor Swift following a naming competition with local schoolchildren.
The second of the 72m tall structures is due to arrive in the coming weeks.