The supermarket giant's technical director Tim Smith said new DNA testing would be introduced for all of its meat products to avoid similar mistakes happening again.
He said: "The evidence tells us that our frozen burger supplier, Silvercrest, used meat in our products that did not come from the list of approved suppliers we gave them.
"Consequently we have decided not to take products from that supplier in future.
"We took that decision with regret but the breach of trust is simply too great."
Silvercrest says that it has "never knowingly bought or processed horsemeat", and insists that all of its purchases are from approved and licensed EU plants.
Around two weeks ago Tesco and a number of other supermarkets removed certain brands of frozen beefburgers from their shelves, after they were found to contain horsemeat.
A study examining the authenticity of a number of beefburger, beef meal and salami products available from retail outlets in Ireland found horsemeat accounted for approximately 29% of the content in one sample of Tesco Everyday Value Beef Burgers.
The findings sparked a national outcry and 10 million burgers were taken off shelves as a result of the scandal.
Mr Smith added: "Ultimately Tesco is responsible for the food we sell, so it is not enough just to stop using the supplier.
"To underpin the strong measures already in place, we will now introduce a comprehensive system of DNA testing across our meat products. This will identify any deviation from our high standards."