Health campaigners joined those praising Chancellor George Osborne for the surprise move, which goes against previous thinking from Prime Minister David Cameron.
Shares in listed drinks firms dropped sharply on the London stock market after the announcement in the Budget.
The tax will be levied against firms that produce sugar-sweetened drinks and brought in in two years' time to give them a chance to drive down their sugar content.
It is part of a wider strategy from the Government to tackle Britain's childhood obesity problem.
Oliver took to Twitter and Instagram to praise the plan, saying on Instagram: "We did it guys!! we did it!!! A sugar levy on sugary sweetened drinks ...... A profound move that will ripple around the world ....business can not come between our Kids health !!
"Our kids health comes first ..... Bold, brave, logical and supported by all the right people....now bring on the whole strategy soon to come ... Amazing news."
The tax is expected to raise £520 million which will be used to double the amount of funding for sport in every primary school, with secondary schools encouraged to offer more sport as part of longer school days.
Tory MP Sarah Wollaston, who chairs the Commons health committee, said on Twitter: "Delighted to see action on sugary drinks in #Budget2016 in a way which encourages reformulation & boosts Childrens sport funding. Drinks like Coke & Pepsi contain 10.6g sugar/100ml so now a clear incentive to reduce below 8g."
Simon Stevens, chief executive of NHS England, said: "This bold and welcome action will send a powerful signal and incentivise soft drinks companies to act on the health consequences of their products.
"Obesity now affects one in five children, causes one in five cancer deaths, and already costs the NHS £5 billion a year - so obesity is the new smoking."
Chris Askew, chief executive of Diabetes UK, said the tax "should not be absorbed by the soft drinks industry".
He added: "Prices need to change, otherwise there will be no impact on the health of nation."
Malcolm Clark, co-ordinator of the Children's Food Campaign, said: "This is a really important victory for children's health. Not only will this tax on sugary drinks encourage people to shift towards healthier drinks, but it sends out a wider message about our need to cut down on sugar, and for businesses to reduce the sugar in their products."
Jonathan Isaby, chief executive of the TaxPayers' Alliance, said: "It is ludicrous that the Chancellor decided to cave in to the demands of the High Priest of the Nanny State in the public health lobby and introduce a hugely regressive and entirely ineffective sugar tax. This will hit the poorest families hardest and all the evidence shows it simply won't work."
Mr Osborne told MPs that obesity costs the economy £27 billion a year.
He added: "One of the biggest contributors to childhood obesity is sugary drinks. A can of cola typically has nine teaspoons of sugar in it. Some popular drinks have as many as 13. That can be more than double a child's recommended added sugar intake."
He said manufacturers recognised there was a problem and had started to reformulate their products with less sugar.
"Robinsons recently removed added sugar from many of their cordials and squashes. Sainsbury's, Tesco and the Co-op have all committed to reduce sugar across their ranges. So industry can act, and with the right incentives I'm sure it will."
But Mr Osborne said he was "not prepared to look back at my time here in this Parliament doing this job and say to my children's generation: I'm sorry. We knew there was a problem with sugary drinks. We knew it caused disease. But we ducked the difficult decisions and we did nothing."
He said the new tax will be assessed on the volume of the sugar-sweetened drinks produced or imported by firms.
"There will be two bands - one for total sugar content above five grams per 100 millilitres; a second, higher band for the most sugary drinks with more than 8 grams per 100 millilitres," he said.
Pure fruit juices and milk-based drinks will be excluded from the tax.
Mr Osborne said some firms "may choose to pass the price onto consumers and that will be their decision, and this would have an impact on consumption too."
British Soft Drinks Association director general Gavin Partington said: "We are extremely disappointed by the Government's decision to hit the only category in the food and drink sector which has consistently reduced sugar intake in recent years - down 13.6% since 2012.
"We are the only category with an ambitious plan for the years ahead - in 2015 we agreed a calorie reduction goal of 20% by 2020. By contrast, sugar and calorie intake from all other major take home food categories is increasing - which makes the targeting of soft drinks simply absurd."
Roger White, the chief executive of AG Barr, whose biggest brand is Irn-Bru, also described the move as "extremely disappointing".
He said: "At AG Barr we have reduced the average calorific content across our brand range by 8.8% in just four years and are actively contributing to the soft drinks industry-wide five-year target to make a 20% reduction by 2020.
"We will await further details and ensure that we are fully involved in the consultation process to ensure our position, and progress to date, are well understood."
Food and Drink Federation director general Ian Wright said: "For nearly a year we have waited for a holistic strategy to tackle obesity. What we've got today instead is a piece of political theatre.
"The imposition of this tax will, sadly, result in less innovation and product reformulation, and for some manufacturers is certain to cost jobs. Nor will it make a difference to obesity. Many of those singled out today by the Chancellor have been at the forefront of efforts to provide consumers with healthy choices. The industry will now ask whether such efforts are still affordable."
The tax means manufacturers of drinks with 5g of sugar per 100ml and more than 8g per 100ml will face a tax.
Sir Harpal Kumar, Cancer Research UK's chief executive, said:"Making sugary drinks more expensive and less appealing to children is a vital step in reducing obesity levels in the UK.
"Our research has revealed that a tax like this could prevent millions from becoming obese. Failing to act would lead to hundreds of thousands of obesity-related cancers in the future.
"We're delighted that Government have listened to Cancer Research UK and more importantly to the public who wanted to see decisive action to prevent the next generation becoming obese."