The petition, calling for a tax of 7p per regular-sized can of soft drink, has been signed by 120,256 people since Oliver launched it last week.
Parliament considers all petitions that gain more than 100,000 signatures.
Oliver, who believes the move could generate £1bn a year to help curb childhood obesity, took to Twitter to thank those that had signed the petition.
“We did it,” he wrote on the social networking site. “To the 100,000 + ‘loverly’ people in the UK thank you for signing and supporting the petition.”
Largest source of sugar
Studies show that soft drinks with added sugar are the largest single source of sugar in the diets of UK school children and teenagers, Oliver said in a joint statement with food lobbying organisation Sustain.
Tooth decay caused by sugar is the main reason children aged five to nine years are admitted to hospital and type-2 diabetes is costing the National Health Service around £9bn a year, they claimed.
Restaurant chain Leon and Oliver’s own restaurants have already put a 10p levy on drinks with added sugar.
The Food and Drink Federation said although it welcomed a parliamentary debate, taxes were not the answer to tackling the obesity issue.
Ineffective and flawed in concept
FDF director general Ian Wright told FoodManufacture.co.uk: “We welcome the prospect of a parliamentary debate on sugar taxes and maintain the view that they have been shown to be ineffective and flawed in concept.
“Additional taxes are not the answer, a view shared by the Department of Health which continues to rule out a sugar tax."
Now was, however, the time for a national conversation about the nation’s health based on science and evidence, Wright added.
“Robust science and evidence must be at the very heart of this debate if it is to inspire collaborative action capable of tackling obesity over the long-term,” he said. “This is, after all, what we all want to achieve.”
Last week, the FDF slammed Oliver for over-simplifying the obesity debate and accused him of double standards for taxing sugary drinks but not displaying nutritional information in his restaurants.