Under the all-share deal, Alcatel-Lucent shareholders will own 33.5% of the new combined company, and Nokia shareholders 66.5%.
Both companies said their boards had agreed the takeover and they expected it to go through in the first half of 2016.
The merger will form a European telecoms equipment group worth more than €40 billion.
Nokia CEO Rajeev Suri said the companies’ complementary technologies would give them “the scale to lead in every area in which we choose to compete”.
“I firmly believe that this is the right deal, with the right logic, at the right time,” Rajeev Suri said.
Nokia and Alcatel-Lucent are currently among the weakest players in the telecoms equipment industry. However, the combined company will have a market share of 35%, making it second only to Swedish rival Ericsson, which has 40%, according to Bernstein Research.
The companies expect the merger to cut operating costs by €900 million by 2019, but Nokia said it would not cut jobs beyond what Alcatel had already planned.
“No job cuts” in France was the condition under which the French government said on April 14 that it would back the deal.
Alcatel-Lucent’s shares fell 10% in early trading, with traders attributing the fall to shareholders’ disappointment that the deal did not have a cash element.
However, Nokia’s shares rose almost 5%, despite some analysts saying that the deal could take a long time to pay off.
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