The acquisition, which is a part of a €12.35bn deal signed by the two companies in 2014, represents the largest ever industrial acquisition by GE.
However, the final purchase price was reduced to €9.7bn following changes made to the deal to secure the approval. Alstom has agreed to reinvest in joint ventures.
GE chairman and CEO Jeff Immelt said: "The completion of the Alstom power and grid acquisition is another significant step in GE’s transformation.
"The complementary technology, global capability, installed base, and talent of Alstom will further our core industrial growth."
GE expects the integration of its power generation technologies, services and expertise with Alstom power unit’s technology and geography to boost the global energy utility sector.
With the acquisition, GE Power will have a diverse portfolio of technologies and services, which will ensure that power is affordable, reliable and sustainable for the customers.
GE Power president and CEO Steve Bolze said: "We now offer utility and industrial power plant operators even more complete, customized ‘one-stop shop’ solutions — not just for developing new stations but also optimized life cycle support for existing facilities to support local energy security.
"Our portfolio of technologies include the world’s largest and most efficient gas turbine — the HA, full power plant components, boilers, steam turbines, reciprocating engines and more.
"Being a digital industrial business, we also offer digital and software solutions, specifically our Digital Power Plant, which helps our customers increase output, improve efficiency, lower operating costs, improve integration of renewable energy and reduce unplanned downtime."