The Moray business did not reveal how much it is paying for the Burntwood site, which specialises in supplying private label, wholesale and food service products.
Japanese firm Nakano agreed to sell the facility, which employs 58 people, to alleviate competition concerns following its £41 million acquisition of the vinegar and pickles business of Premier Foods Group in June last year.
As a result of the deal with Baxters, the Office for Fair Trading (OFT) has decided not to refer the Nakano and Premier Foods deal to the Competition Commission.
The OFT said it had consulted publicly on the proposals, including the suitability of Baxters as the buyer, and had not received any concerns regarding the transaction.
Yesterday, Ali Nikpay, OFT senior director and the decision maker in the case, said: "The OFT was concerned that prices of unbranded malt and spirit vinegar would rise as a result of Nakano's acquisition of Premier's vinegar business.
"The sale of the Burntwood plant to Baxters restores pre-existing levels of competition in the manufacture and supply of these vinegars to UK customers."
Family-owned Baxters is best known for its soups and preserves, but in November 2011 it bought the canned meat pie brand Fray Bentos. Princes, which had bought Fray Bentos from Premier, sold the brand after OFT concerns.