The contract is reported to be worth around €15m annually to Silvercrest, based in Co Monaghan.
The retailer made the announcement on Wednesday after it launched an investigation.
"We made a commitment to customers to investigate thoroughly and share the findings with them," Tim Smith, Group Technical Director said.
"Since then, we have been working hard to understand what happened and how we can stop it ever happening again."
Silvercrest did not source meat from suppliers approved by Tesco, the supermarket claimed in the statement.
"Nor was the meat from the UK or Ireland, despite our instruction that only beef from the UK and Ireland should be used in our frozen beef burgers," it continued.
The retailer has said it will not be working with Silvercrest in future.
We took that decision with regret but the breach of trust is simply too great.
Tim Smith, Tesco group technical director
The director said that Tesco will be introducing a "comprehensive system of DNA testing" across their meat products in addition to their "stringent tests" already in place.
"These checks will set a new standard. It will be a significant investment for Tesco, borne by Tesco.
"We want to leave customers in no doubt that we will do whatever it takes to ensure the quality of their food and that the food they buy is exactly what the label says it is."
President of the Irish Farmers Association, John Bryan said despite the bad publicity Tesco has assured them that it will continue to buy Irish products.
He said: "We've been in discussion with them over the last few weeks and the last few days, where they assured us that they're going to continue to purchase the same volume of food from the Irish producers, but they are no longer going to do business with Silvercrest."
Two weeks ago Food Safety Authority of Ireland (FSAI) revealed that scientific tests found traces of horse DNA in frozen burgers on sale in some of the UK and Ireland's leading supermarkets.
The survey uncovered low levels of the DNA in most products, which were sold in Tesco, Lidl, Aldi, Iceland and Dunnes Stores.
However it showed that the Tesco's Everyday Value Beef Burgers, which were tested by the FSAI, contained about 29% of horse meat relative to beef content. They also tested positive for pig meat and have been sold in Tesco stores in Ireland and the UK.
The retailers have told food safety chiefs they removed all implicated products from their shelves.
Following tests, the Republic's Agriculture Minister, Simon Coveney, said the meat most likely came from raw material imported from Poland.
On Wednesday, Food Standards Agency (FSA) chief executive Catherine Brown told the Environment Committee at Westminster that it was possible the product containing the horse meat could have been in the food chain for up to a year.
"The probable limit of possibility..is a year because it's been a year that this supplier has been supplying," she said.
"And therefore when the Polish get to the bottom of this we will hope to know whether it's likely that this has been going on for a year."
She added that there was currently no evidence that the food was unsafe.
The ABP Food Group has developed a very strong business - based on trust. We have let our customers down in this incident and we apologise for this.
ABP Food Group statement
Silvercrest, a subsidiary of ABP Foods pulled the products in question from sale and replaced them with new lines.
The company said they had never knowingly purchased or traded in equine products and pledged to introduce a new testing regime in the wake of the scandal.
ABP Food Group said they understood the supermarket's decision but welcomed the fact they will continue to source fresh beef from their other companies.
CEO Paul Finnerty said: "We have learnt important lessons from this incident and we are determined to ensure that this never happens again".
He said they have already implemented total management change at the Silvercrest facility - which remains closed.
In a statement, the company said that a group re-organisation has taken place to better manage the business, as well as new procedures to audit third party suppliers and comprehensive DNA testing procedures have been established.
"We are proud of our excellent reputation for quality and service throughout Europe and are determined not to allow the Silvercrest incident to overshadow what is a great business," the statement said.
"We thank our customers for their continued support at this time."