The €750m (£596m) deal was completed on 31 October and also has the approval of US competition authorities.
As a result, Sappi has expanded its woodfree coated products and increased its European graphic paper capacity from 2.6m tonnes per annum to 4.5m tonnes per annum.
The acquisition, which is expected to be completed following a rights issue during the first quarter of 2009, will make Sappi the number three player in the market.
Sappi chief executive Ralph Boëttger said: "We are delighted that the European Competition Commission has given its approval for this transaction.
"It is a strong stamp of approval for our acquisition and paves the way for us to drive long-awaited consolidation and transformation of the European coated fine paper sector, while creating significant value for Sappi shareholders."
In September, South African company Sappi agreed to acquire M-real's coated graphic paper business.
The sale includes the purchase of M-real's coated graphic paper mills Kirkniemi and Kangas in Finland, its Stockstadt mill in Germany and its Biberist plant in Switzerland - a total capacity of 1.9m tonnes.
Sappi's M-real bid gets green light from competition bodies
The EU competition authorities have cleared Sappi's proposed acquisition of M-real's coated graphic paper business.