The competition watchdog said the move would not limit competition among the wind industry's big players and suppliers.
"[GE] has a relatively small market share in both onshore and offshore wind turbines. Although LM Wind Power has a significant market share, its market position has been decreasing in the past few years, and in-house blade production also has to be taken into account," the authority said.
It added that other blade manufacturers would continue to have access to other turbine manufacturers. Meanwhile the major OEMs, such as Siemens, MHI Vestas, Vestas, Nordex and Senvion were not dependent on LM Wind Power and some produce blades in-house.
GE announced the €1.5 billion takeover in October 2016, after reaching a deal with LM Wind Power owner, private equity firm Doughty Hanson.
GE said it intends to operate the blade manufacturer as a "standalone unit" under its renewable energy business.
The US-based firm will "continue to fully support all industry customers with the aim of expanding these relationships", it said.
LM is set to break ground on a new factory in Cherbourg, France, later this week, which will be used to supply the offshore wind sector.
The new factory will be able to produce LM's 88.4-metre offshore wind blades, revealed in June last year.
The world's longest turbine blade was designed for Adwen's 8MW offshore wind turbine, which has a pipeline of around 1.5GW in France.
The EC's approval of the takeover comes a week after it gave the go-ahead for Siemens' merger with Adwen-owner, Spanish manufacturer Gamesa.