The company said 930 dairy farmer suppliers have agreed to no longer export dairy calves to continental Europe where welfare standards are said to be below those required in Britain.
Instead the UK-reared calves will be used to boost the supply of British beef and replace current sales of veal in Tesco stores.
The move follows similar announcements made by other British retailers in recent months and highlights the impact of media coverage of animal welfare and growing consumer attention to the sourcing of food products.
In October, Marks & Spencer said it was banning imported white veal and calves' liver from its stores, promising to sell only rose veal bred in the UK under decent welfare standards from this month.
Animal welfare campaigners say that calves bred for veal meat are reared in small, cramped crates that restrict their movement and growth of muscle.
They are fed on a nutritionally poor milk diet, giving the meat its white colour.
Tesco and M&S say British-produced rose-coloured veal comes from animals reared in well-lit barns with straw beds and fed a natural diet.
Figures for current consumption of veal in the UK were not available at time of publishing but it is likely to be small after years of campaigns designed to show the cruelty involved in producing veal under traditional methods.
In an opinion poll carried out by GfK NOP and published by the campaign group Compassion in World Farming in January 2007, 75 per cent of customers believed that British calves should be reared and slaughtered in the UK.
But thousands of dairy calves not needed in Britain are exported to Europe to feed much bigger veal consumers.
Welfare groups say that live, young calves are exported in cramped conditions for up to 100 hours.
"Independent research shows that the majority of shoppers want this practice to end," said Tesco dairy category director Kari Daniels.
A major campaign to change farmers and consumers' attitudes to veal is also set to be launched today, according to a report in The Guardian.
It will attempt to demonstrate the benefits of eating British-reared veal, which is said to be a healthy option for consumers.
Live exports to the Continent had been banned after a foot and mouth outbreak in the UK but since starting up again in December, animal welfare campaigners have renewed pressure calling for an end to live calf exports.