Close to 9,000 jobs, or about 10% of the companies' workforce will lose their jobs as a result of the merger. Analysts said the deal is a good fit, giving the two firms the chance to expand in both Europe and the US.
Alcatel and Lucent had tried to merge five years ago, but talks collapsed. This time round they had to overcome concerns about security because Lucent does work for the US government.
To smooth the merger's path, Lucent will set up a separate US company to deal with sensitive government contracts. It also was complicated by Alcatel's plans to boost its stake in Thales, a French defence electronics group that does work for the government.
Alcatel said the talks would continue with Thales, which is 30%-owned by the French state.
The new company, which has yet to be named, will be based in Paris and incorporated in France. Lucent's chief executive Patricia Russo will head up the new firm, while Alcatel's boss Serge Tchuruk will become non-executive chairman.
Alcatel said it joined forces with Lucent because competition in the telecoms market was intensifying. "The primary driver of the combination is to generate significant growth in revenues and earnings based on the market opportunities for next-generation networks, services and applications," the companies said. Ms Russo said that: "This is an industry where size and scale matter."
Analysts said that the merger between Alcatel and Lucent could spark a spate of consolidation in the industry. Paris-based Alcatel is one of France's leading telecoms suppliers, servicing internet service providers and broadband providers. It employs 58,000 staff in 130 countries and generated sales of 13.1bn euros ($15.6bn; £9bn) last year.
Lucent, which is headquartered in New Jersey, has more than 30,000 employees and sales of $9.4bn. The firm, which used to be part of US telecoms giant AT&T, suffered severe financial problems after the tech bubble burst in 2001.