The first tram to run on streets at normal speed in daytime traffic reached Princes Street shortly after 3pm on its way to the end of the line at York Place, off St Andrew Square.
The latest stage of tram testing, as revealed by The Scotsman two weeks ago, comes three months before they are due to come into passenger service.
It follows night-time testing since December on the £776 million, eight mile route from Edinburgh Airport.
Ms Hinds said: “Like a lot of people who were tweeting about it, I was very excited to spot the tram from my office window as it travelled along Princes Street and back again today.
“It’s a historic moment for Edinburgh and reflects a key moment in the project where we’ll now begin to see more and more trams out on the full route during the day as we push on with the testing, commissioning and driver training programme.”
Tom Norris, Edinburgh Trams’ director and general manager, who accompanied the driver on the test run, said: “It was quite something being on board as we brought the tram into the on-street section for its first daytime test.
“Like the first night-time tram, it seemed to generate lots of interest - most people’s first response seemed to be to reach for their phone or camera and get a picture.
“Today’s test is the latest in a comprehensive programme of system testing and driver training.
“We’re looking forward to getting more and more drivers used to daytime on-street road and traffic conditions over the coming weeks.”