Both GPC and CLV are currently owned by another French group, 3A. The price paid has not been disclosed.
The Commission said that although Lactalis and the 3A businesses had overlapping operations, their combined market shares remained modest, meaning that the takeover could proceed as planned.
First announced back in June, Lactalis said that the acquisition of the two Spanish businesses would add around €260 million in sales and give it four local production facilities. The units specialise in liquid milk production, churning out around 480 million litres a year.
As well as owning one of the top milk brands in the Madrid region - Lauki - the 3A businesses also own the country's biggest horchata brand, Chufi. Horchata is a popular drink made from chufa, a tuber that grows on the roots of the sedge plant found in southern Spain, and is becoming extremely popular elsewhere as a result of its health benefits - including a high vitamin E content.
The 3A businesses also own the second biggest Spanish flavoured milk brand, Choleck.
Lactalis has been active in Spain for 20 years, and also produces liquid milk - some 115 million litres of it each year, to be precise. The deal will allow it to gain a bigger share of a Spanish milk market which remains highly fragmented, in particular strengthening its popular President brand.
The merger of 3A with Lactalis Iberia will create Spain's second largest dairy group after Central Lechera Asturiana (CLAS). Lactalis beat off a trival bid for 3a from Dean Foods, the US group which owns the Leche Celta brand in Spain.