The commission, which was investigating whether the merger could lead to price rises across the brands' key ketchup and sauces sector, has said that the deal has been given a provisional clearance ahead of a final report due in April.
It found that even though the brands shared a number of products, there was little competition and price hikes were unlikely.
Robert Turgoose, chairman of the inquiry group, said: "In spite of the increased size of the merged company, we do not expect a substantial loss of competition or an increase in prices to result from the merger."
He said, in particular, HP's brown sauce product and Heinz's ketchup range appeal to different customer profiles and are used with different foods.
With both brands' barbecue sauce products, because these are not seen as "must stock" items by retailers, the merger would have little affect on prices.
The potential affect on the food service market was also investigated, but it was found that HP competed with Heinz only on a limited basis.
William R Johnson, Heinz chairman, president and CEO, said: "Heinz is delighted with the initial findings of the Competition Commission and we continue to cooperate fully with them as they review the merits of our acquisition of HP Foods.
"These initial findings are in line with our expectations and we remain confident that this acquisition will meet the criteria for final clearance."
This latest announcement comes as Heinz completed the sale of its European seafood business, a significant milestone in its strategy of concentrating on its core businesses, including ketchup.
The seafood portfolio, which includes the John West canned fish brand, was sold to Lehman Brothers Merchant Banking in a £290m deal.
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