A ban on tobacco firms using branded goods such as clothes to advertise in the UK comes into effect on Monday.
Grand Prix racing attracts many millions of pounds in sponsorship
The move coincides with the start of an EU-wide ban on sponsorship of sporting events by tobacco firms.
Sunday's Hungarian Grand Prix was the last race in an EU country to feature tobacco advertising - banned from the British Grand Prix since 2002.
The 2006 snooker World Championship will be the first in 30 years not to be sponsored by Embassy cigarettes.
The EU directive also bans tobacco advertising in the print media, on radio and over the internet.
The Department of Health hailed it as a landmark in the protection of public health, saying it was determined to see an end to tobacco advertising in motor racing.
It is estimated that banning tobacco advertising, promotion and sponsorship will result in a 2.5% drop in the number of deaths caused by smoking, eventually saving as many as 3,000 UK lives a year.
Degree of uncertainty
The UK government has taken the EU rules a step further, banning firms from using goods such as T-shirts, hats or pub umbrellas from advertising tobacco products, under the final stage of implementation of the Tobacco Advertising and Promotion Act.
It remains unclear what the new EU rules will mean for sporting events held outside the union but broadcast within it, BBC business correspondent Richard Scott says.
Advertising tobacco products on TV in the UK has been banned since the mid 1990s.
Tobacco advertising in shops and newsagents was outlawed in December 1999 and tobacco sponsorship of sports ended in 2003.
The government has stepped up its anti-smoking campaign
A spokeswoman for anti-smoking campaign group Ash welcomed the sports sponsorship ban but said she feared tobacco-sponsored motor racing from the wider world would be televised in EU countries.
She said: "The real problem is that Formula One is so popular worldwide. What is not clear is whether the ban will extend to the broadcasting of tobacco-sponsored Formula One races from outside the EU to EU countries.
"If that is the case the spirit of the law will be undermined."
After the British Grand Prix advertising ban came into effect, some tobacco producers switched to using logos or colour schemes similar to their usual adverts to promote their products at races.