Both entities had entered into an agreement for the deal, which is on slump sale basis, in March. BSA International would buy Anik Industries' dairy business that includes manufacturing, marketing and distribution of milk and related products.
Part of the Lactalis group, BSA International is present in India through its subsidiary Tirumala Milk Foods.
Clearing the deal, the fair trade regulator said it is unlikely to have an adverse impact on competition in the Indian market.
Anik Industries is engaged in the business of dairy products, power generation and trading of coal and agro commodities.
"The Commission is of the opinion that the proposed combination is not likely to have an appreciable adverse effect on competition in India," it added.