The deal is in line with the strategy to have autonomous journeys account for 25 per cent of total individual journeys in Dubai by 2030.
The agreement also reflects RTAs efforts towards providing driverless transportation solutions through undertaking technological tests of autonomous transit means, Mattar al-Tayer, RTA director general, said in a statement.
The contract, worth an estimated $17m to $20m based on list prices of the Tesla model S and X cars, was signed on the sidelines of the ongoing World Government Summit in Dubai.
Tesla opened its Middle East regional office in Dubai on 13 February. A dedicated website that takes orders from UAE customers has also been launched, along with a store in Dubai Mall and a roving technician service. A service centre is also under construction near the Second Interchange on Sheikh Zayed Road.
Tesla said it expects to make the first deliveries this summer.
It plans to open a store and service centre in Abu Dhabi in 2018.
Supercharging stations, which utilise technologies that allow charging of electric car batteries in minutes rather than hours, have also been installed at the last exit in Jebel Ali and in Masdar City in Abu Dhabi.
France-based Engie has already installed electric car battery chargers in eight hotels across the UAE.
Earlier this month, France-based Axa Isurance announced an insurance product tailored for Tesla cars.
The price of the policy will be within the maximum rates imposed by the Insurance Authority of 5 per cent of the car value for sedan-type cars, Axa said.
In January, Emirates NBD rolled out a loan product tailored for electric cars. The loan rate is 25 percentage points lower than loans designed for regular cars.
The bank also said they are hoping for the UAE Central Bank to consider extending the five-year loan cap for regular cars to seven years for electric cars.
Price list for the Tesla model S starts at $74,800 (AED275,000), while the model X starts at $93,600.