The legal minimum age at which tobacco can be bought in England, Scotland and Wales has gone up from 16 to 18.
The move is designed to cut teenage smoking rates
The government hopes the move will reduce the number of young people who smoke and make it easier for retailers to spot under-age smokers.
Earlier this year it launched a website and advertising campaign aimed at teenagers to highlight the change, which came into force on Monday.
The move follows the banning of smoking in public places in the three nations.
About 9% of 11 to 15-year-olds smoke, and ministers hope the move will reduce this figure.
Ministers believe that bringing the age for the purchase of tobacco into line with that of alcohol will reinforce the dangers of smoking to young people.
It will also bring England, Scotland and Wales into line with Canada, Australia, New Zealand and the US.
Research has suggested that only a quarter of children aged under 16 who tried to buy tobacco found it difficult to do so.
Retailers that stock tobacco will have a legal obligation not to sell to under 18s and will risk prosecution and a fine of up to £2,500 if they do so.
But the government's advertising campaign has been criticised as "woefully inadequate" by the Association of Convenience Stores, which represents about 33,000 local shops.
Its chief executive James Lowman said: "Awareness appears to be worryingly low - research shows that one in five 16 to 18-year-olds are not aware of this change.
"The risk that low awareness presents is that people will blame the retailer for refusing to sell them a product they were previously able to buy."
The move to raise the legal age for purchasing tobacco has been welcomed by the campaign group Ash.
Amanda Sandford, Ash's research manager, said proper enforcement was key to its success.
"It is imperative that retailers fully comply with the law and that enforcement officers make frequent checks on premises selling tobacco," she said.
Simon Clark, director of the smokers' lobby group Forest, said measures to discourage children from smoking were welcome, but felt ministers were guilty of sending out mixed messages.
"You're considered old enough to have sex at 16, drive a car and join the army at 17, but the Government doesn't want you to smoke until you're 18," he said.
A spokeswoman for the Department of Health said: "We ran a very targeted age of sale awareness campaign, aimed at the primary audience of retailers and 16 to 17-year-old smokers, who represent approximately 0.5% of the population.
"It is important that we spend taxpayers' money wisely on targeting the key audiences on this issue.
"The age of sale legislation shows our commitment to continue to drive down smoking rates in the UK as smoking remains the number one cause of ill health and early death."