Testing during the day had previously been carried out only between Edinburgh Park and the airport.
After more than six years of construction, the trams are due to begin transporting passengers by May and drivers, pedestrians and cyclists are being warned to be alert as testing is stepped up.
Councillor Lesley Hinds, transport convener for Edinburgh Council, said: "Until now, trams have been running only at night when the city centre roads are much quieter.
"Daytime tests are not far away and it will take some time for people to get used to seeing trams running on streets, so we are asking drivers, pedestrians and cyclists to take extra care while everyone becomes familiar.
"I have seen first hand in Dublin how trams interact with traffic and, as progress continues to be made along the route, it will be important that people are aware of the differences.
"The target launch is drawing ever closer, but there are still many important tests and a driver training programme to complete."
Multiple tram test journeys will be carried out along the full line this week.
The council and Transport for Edinburgh have produced a series of online safety videos and tips as part of an awareness campaign as the launch date approaches.
Tom Norris, director and general manager of Edinburgh Trams, said: "Our team have been training extremely hard and we are ready to move into a phase where many more trams start to run along the route.
"Safety is our first priority and our drivers are all fully aware that other road users need time to get used to interacting with the new trams."