The Japanese industrial conglomerate said it would pay €773 million ($875 million) for the Italian firm's 40 percent stake in Ansaldo STS, the world's number two traffic signal company, and €36 million for struggling rail car unit AnsaldoBreda. Hitachi said it would also bid for the remaining shares of Milan-listed Ansaldo STS that Finmeccanica does not already own.
Japanese media earlier reported that the deal, which is expected to be closed later this year, could top $2.0 billion.
Hitachi, which fell 0.77 percent to finish at 828.2 yen in Tokyo, is looking to boost its global operations after its key nuclear unit took a hit following the 2011 Fukushima nuclear crisis.
The acquisition will push up Hitachi's annual rail-related sales to more than 400 billion yen - about half that of Canada's Bombardier, Siemens of Germany or France's Alstom, the leading Nikkei business daily reported earlier on Tuesday.
Last week a consortium, including Hitachi and Japan's top heavy machinery maker Mitsubishi Heavy Industries, struck a $3.36 billion deal to build Qatar's first subway system.
"The acquisitions represent a key milestone in Hitachi Rail's strategy to become a global leader in total rail solutions," Hitachi and Finmeccanica said in a joint statement.
"The businesses acquired are strategically important for Italy and the combination with Hitachi will also provide a unique opportunity to pursue untapped growth potential in new markets."
Hitachi and three other companies stepped forward as prospective buyers after Finmeccanica announced plans last summer to unload the two subsidiaries. The Japanese firm came close to sealing a deal last November, but a subsequent offer from a Chinese company delayed Finmeccanica's final decision.
The purchase is the latest step in Hitachi's long-running pursuit of the two companies, with Italian media reporting in March 2012 that the conglomerate was interested in buying the firms.
Genoa-based Ansaldo STS, which had sales of €1.3 billion last year, has about 4,000 employees in more than 30 countries. Naples-headquarted AnsaldoBreda has about 2,300 employees and makes a range of trains including those for subways and high-speed routes. It is supplying a fleet of driverless trains for Milan's metro.