The longest of the slides, entitled "Test Site", is more than 55m long and drops steeply from the fifth floor of the museum, housed in a former power station on the banks of London's River Thames.
The slides are the work of Carsten Hoeller, the German conceptual artist, and the Tate Modern expects that around 1,200 people each day will ride them for free from now until April next year.
The opening day saw dozens of tourists, schoolchildren and office workers on their lunch breaks queuing for tickets for the slides, which can vary in speeds.
Steve Malone, 35, an information technology worker from London, said he had been to all the previous grand-scale installations in Tate Modern's Turbine Hall and Hoeller's slides were "the best one".
"This is what we need in art galleries, something to put smiles on peoples' faces," he said.
Another worker taking advantage of the slides was Simon Wood, 27, a market researcher who came to the gallery during his lunch break after seeing an item on the news.
However, he had one minor complaint about the slide he went on.
"This is what we need in art galleries, something to put smiles on peoples' faces"
"It's not quite wide enough so I got stuck on the way down," he said.
Occasionally, people came off the metal slides, hitting themselves on the way down despite riding on mats.
However, a Tate Modern spokeswoman said that a full health and safety assessment had been carried out.
Safety precautions are also in place, including a ban on children shorter than 1.4 metres and riding head first down the slides.
Slides have become one of Hoeller's trademarks; he built one at the Milan headquarters of fashion house Prada in which boss Miuccia Prada uses to slither down from her office to a waiting chauffeur-driven car.
Hoeller wants slides to be taken seriously as a mode of transport and believes they can be used to fight stress, depression and other mental health problems.