Pictures show the 10-metre long object - which generates power through a rotational force created by water moving from high to low - being lowered into position on Tuesday October 1st.
The part, which arrived from Holland earlier this week, brings the micro-hydro scheme a step closer to full operation to ensure the park is fully eco-powered.
It is expected that the electricity in the park will be hydro-powered from early 2020.
Ground source heating is already being used in the park's buildings and glasshouse and the hydro-power generated by the Archimedes screw, using water directly from the Water of Leith, will provide electricity across the park.
Combined with the two ground source heating installations, the micro-hydro scheme will prevent over 90 tonnes of CO2 being pumped into the atmosphere each year.
And it will generate enough energy to power the whole park, including lighting and buildings such as the new cafe which should open later this year.
The micro-hydro scheme project was partially financed thanks to £482,107 from the SP Energy Networks Green Economy Fund.
The project is part of the Saughton Park restorations which is costing £8 milllion.
Councillor Donald Wilson, Culture and Communities convener, said: "What an incredible milestone this is, not just for Saughton Park but for Edinburgh as a whole.
"Having been instrumental in bringing this forward and pushed it for over a decade I am delighted to see it become a reality. We've set ourselves a hugely ambitious target of becoming carbon neutral by 2030 and projects like this are just the kind of innovative, collaborative, multi-partner model we need to see more of in the Capital.
"The Archimedes screw has been installed as part of the micro-hydro scheme and I know it will be a real draw for visitors to this already fabulous and much-loved park."
Green councillor Gavin Corbett said: “For a Green councillor and, I am sure, for many others, the arrival of a reverse Archimedes screw turbine is like a visit from Santa.
"Once up and running at the weir beside Gorgie Road it will provide electricity for the park and also power the ground source heat pumps which keep the glass houses and buildings warm. So Saughton Park will work off locally-sourced renewable energy.
“It is yet another feather in the cap for the park and also a fantastic nod to the historical role of the Water of Leith as Edinburgh’s power-house."