The massive 1.7 million pounds hydroelectric project is expected to start generating electricity from the New Year, powering Windsor Castle as well as more than 300 homes.
It has taken years for the scheme to get off the ground after previous attempts failed because of problems with funding.
The Archimedes screws are the biggest project to date as part of a wider drive by the Royal Household to both cut bills and reduce their carbon footprint.
The Queen has struck a deal with a power company to buy the electricity generated by the turbines to heat and light her home.
Though details are confidential The Queen will save "a huge amount" on her electricity from the hydro scheme under the deal.
The Queen wanted to start cutting the bills at Windsor with electricity generated from the Romney Weir hydroelectric project.
The project will also help the environment as a new 'fish path' has been built alongside the weir to allow fish and eels to migrate up the river for the first time in centuries.
The turbines, which have the appearance of a screw, were developed by the Ancient Greek mathematician and engineer Archimedes of Syracuse.
They cost around 700,000 pounds from a factory in Holland and a further 1 million pounds to install. It is estimated that the turbines will reduce carbon dioxide emissions by 790,000 kilos per year.
The Queen was unable to install the turbines herself as it is on a stretch of the Thames owned by the Environment Agency.
However, the Royal Household is helping to pay for the project by buying the electricity from the developer Southeast Power Engineering Ltd (SEPEL).
David DeChambeau of SEPEL said both the Duke of Edinburgh and the Queen were pleased to finally be going green.
"People have been trying for 20 years to make the hydro scheme happen and hadn't managed it. I said 'I'll get it done in a year," the Telegraph quoted him as saying.
"They are quietly excited by this project at Buckingham Palace. I have met with people from the palace every month and they came out here recently. We will power the castle and with some to spare for local businesses and home," he added.