The service is being run by Loop and the council had earmarked 14 car parking spaces around the edges of the city centre for the company's exclusive use free of charge.
Wright said the car parks were ones that were generally lower use and the council did not expect to have any significant impact on parking supply in the city or on neighbouring businesses.
As well as the public car parks, the company would also use some private car parks.
The trial is expected to start in June 2019 once signage had been put up and the car parks had been re-painted to indicate they were dedicated car share spaces.
Wright said the pilot would be reviewed over the three year period to assess its performance, impact on city parking availability and whether members of the public were using it.
Hamilton City Council chair of growth and infrastructure Dave Macpherson said after one year council would also assess whether it would charge Loop for the car parks.
He said car sharing had the potential to ease traffic in the city, reduce its carbon footprint and supported social inclusion by giving people more affordable access to cars and reducing the need to own one.
"It also makes sense as car share supports the council's Access Hamilton Strategy by providing further options for transport choice in our city."
Macpherson said it was his understanding the cars would be Volkswagen Golfs and run on petrol. However, the company was considering switching to the more expensive electric vehicles at a later stage.
The hourly rental fee was $15 an hour, $75 for 24 hours and $30 to take overnight, according to Loop's website. There are additional charges if users exceed 150km in a 24 hour period.
Users can download the app to their phones and are required to provide a driver's licence and credit card details. Cars can be reserved up to 30 minutes in advance.
Macpherson defended not putting the scheme out to tender to other operators because the company had approached the council. It would likely go out to tender after the trial period.
Lime Scooters are also in the process of rolling out in Hamilton and were also expected to launch in the city in the next few months, Macpherson said.
Loop declined to comment at this stage.