The Price Promise covers both branded goods and own-label products, unlike the price-matching scheme of rival Sainsbury's, which only covers branded products.
Tesco will compare basket prices at Asda, Sainsbury's and Morrisons, and provide a voucher for the difference of up to £10 if rivals are cheaper.
Customers shopping in-store will receive a voucher at checkout, while those shopping online will receive an email within 24 hours.
Price comparisons will also include promotions including "half price" and "buy one, get one free" offers at Tesco and Asda, Sainsbury's and Morrisons.
Three TV executions launch today, supported by a nationwide out-of-home campaign, press executions and online ads.
Wieden & Kennedy has created the campaign, while media planning and buying has been handled by Initiative.
Chris Bush, UK managing director at Tesco, said: "We're working hard to build a better Tesco for our customers in the UK, and Price Promise is an important part of that. It gives our customers complete confidence that they won't lose out by shopping at Tesco.
"We're the first major retailer in the UK to compare our prices against the branded and own-label prices of our competitors and give customers an automatic coupon for the difference."
TV activity is being supported by press advertising using the newly adopted long-copy style used in Tesco's ads apologising for the presence of horsemeat in some of its products.
A press ad claims Tesco will help customers discover whose prices are best and admits, "We've been part of that problem, so it's up to us to figure it out…we're already working on the quality of our food and now we're looking at price".