The deal will cement the Finnish company's aspirations to become a major provider of networking equipment, taking on the likes of market leader Ericsson.
The acquisition will close in the first half of 2016.
It follows Nokia's sale of its mobile hardware division to Microsoft.
A Nokia spokesperson said the combined company would be uniquely positioned to create the foundation of seamless connectivity for people and things wherever they are.
"This foundation is essential for enabling the next wave of technological change, including the Internet of Things and transition to the cloud," a spokesperson said.
"With more than 40,000 R and D employees and a spend of €4.7 billion in R&D in 2014, the combined company will be in a position to accelerate development of future technologies including 5G, IP and software-defined networking, cloud, analytics as well as sensors and imaging."
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Following the acquisition, Nokia will look to achieve a €900 million reduction in operating costs by 2019.
Alcatel employs about 52,000 workers. More than a third of those are in research and development.