The company's board has "acknowledging unanimously the strategic and industrial merits of this offer" Alstom said in a statement. It has set up a committee of independent directors to review the offer before the end of May.
Patrick Kron, Alstom CEO, said: "The combination of the very complementary energy businesses of Alstom and GE would create a more competitive entity to better service customer needs."
The deal would include the renewable power, thermal power and grid divisions, as well as corporate services. Alstom said that if it accepts the offer it would "refocus on its transport activities".
Alstom said it would consider the interests of "all stakeholders" including the French state. Any agreement would also be put before workers' representatives.
Bouygues, a 29% shareholder of Alstom, has committed not to sell its shares, Alstom said, unless board agrees to the deal.
A takeover by GE would have significant consequences for the wind industry, with two major players merging.
If Alstom opts to go with GE, it could have awkward repercussions for Alstom's burgeoning offshore business given the US company's antipathy to the sector.
Earlier this year, GE renewables chief Anne McEntee restated the company had no plans to enter the offshore market.
Siemens confirmed on Tuesday that it will make a bid for Alstom's power business, but has said that it needs four weeks to carry out due diligence before putting an offer on the table.
Alstom said today that Siemens will have a "fair access" to information needed to make a binding offer and it will review Siemens' expression of interest.
The two companies stepped up their efforts to take control of the business on Monday, with Siemens confirming that it sent it CEO to France to meet the president. GE's CEO already met with French President Francois Hollande to discuss the company's planned takeover of Alstom Power.
GE will be keen to allay the fears over the takeover of a major French firm by an American rival. The French government has expressed concern about GE's bid to buy all or part of the French manufacturer, which is a major player in the global wind industry, for a reputed $13 billion.
Alstom is a direct competitor of Siemens in the offshore wind market, with its 6MW Haliade turbine filling a similar space to Siemens' 6MW machine.