Siemens will receive newly issued shares in the combined company representing 50 percent of Alstom's share capital and warrants allowing it eventually to acquire another 2 percent of Alstom shares.
However, the deal prevents Siemens from owning more than 50.5 percent of Alstom for four years after closing, and includes "certain governance and organizational and employment protections", Siemens and Alstom said in their statement.
The deal is unanimously supported by Alstom's board, Siemens' supervisory board and Alstom shareholder Bouygues, the companies said.
The French government acquired its option on the Bouygues stake in Alstom in 2014 as part of a deal that helped Alstom snub Siemens as a buyer for its energy business in favour of General Electric Co.
Macron was economy minister at the time.
The global headquarters, rolling stock business and stock-market listing of the new entity will be in Paris and the signalling and technology business in Berlin.
The new company, with 62,300 employees, targets synergies of 470 million euros four years at the latest after closing of the deal, which is expected at the end of 2018.
The companies said their operations were largely complementary, with Alstom present in growth markets in the Middle East and Africa, India, and Central and South America, while Siemens was strong in China, the United States and Russia.
Siemens CEO Kaeser said ahead of the signing of the memorandum of understanding he believed the scale of China's CRRC left little room for regulators to oppose a deal.
"It always depends, but the facts are that there is a dominant player," he told Reuters in an interview in New York.
Siemens stands to gain control of Alstom's main business, since all of Alstom's divisions deal with the railways and transportation industries. Existing Alstom shareholders will be paid two special dividends: a control premium of 4 euros per share to be paid shortly after closing of the transaction and an extraordinary dividend of up to 4 euros per share to be paid out of the proceeds of Alstom's put options for its General Electric joint venture, "subject to the cash position of Alstom".