The takeover is subject to divestment of Alstom's heavy-duty gas turbine business to Italian firm Ansaldo, said the commission.
Anti-trust regulators found there were no further concerns regarding the companies' renewables and grid business as "the activities of the two companies are complementary and do not overlap".
"I am glad that we can approve this transaction, which shows that Europe is open for business and that Europe-based technology can thrive and attract foreign investment," said EC competition commissioner Margrethe Vestager.
"In my book, this is a big deal," Vestager added.
It is expected GE will include its onshore wind activities in a global renewable energy business group headquartered in Paris. Jerome Pecresse, currently Alstom's vice-president responsible for renewable energies, will head the group.
The new group will also include Alstom's offshore wind assets, plus hydropower and all other renewable energies, combined in a joint venture in which GE will have operational control.
Alstom obtained French government approval for the proposed takeover of its power division by GE, including the creation of an offshore joint venture, in November 2014.
Alstom's 6MW Haliade offshore turbine will be deployed at the 30MW Block Island project, currently under construction in the US. It will be the first commercial project to use the turbine.