One pedestrian said the routes offered a "new perspective" on Dundee, while another said it would "breathe new life" into the Waterfront.
The grid pattern became operational on Friday morning following two years of construction work.
Dundee City Council said the project was completed on time and on budget.
Rod McLeod, 71, from Carnoustie was one of the first pedestrians to use the new route.
He said: "It's excellent. It breathes new life into the area.
"It has been a bit of a nightmare with the roads being changed, but I thought once they got it right it would be good."
Another pedestrian said: "It gives a new perspective on Dundee, it's great."
The new Slessor Gardens beside the routes will be fenced off for the rest of the winter to allow grass and trees to grow.
Contractors Sir Robert McAlpine were responsible for the Â£11m creation of the new routes.
Dundee council leader Ken Guild said: "Once the V&A site is complete and our illustrated fences down there are removed, you will get a straight view right across to the hills of Fife.
"It's really reconnecting the city centre with the river, which is what the whole central Waterfront project is about.
"We've had considerable interest in the various sites either side of Slessor Gardens for mixed-use developments, so that's been very good."
New streets and pavements connecting Dundee Waterfront to the city centre have opened to the public for the first time.