Hitachi announced the plan on Tuesday, in a deal that could reach more than $2.0 billion as it looks to take on global rail giants.
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 euros for struggling rail car unit AnsaldoBreda.
But the acquisition faced immediate opposition from Italian labour unions, with Fiom-Cgil demanding urgent talks with government ministers on the decision.
But with Prime Minister Matteo Renzi keen to encourage inward investment in a recession-bound economy, state interference with the deal is seen as unlikely.
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 close later this year, could top $2.0 billion.
"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."
Finmeccanica CEO Mauro Moretti said the sale of the rail transport business was a key step in the company's plan to focus on the core business of aerospace, defence and security.
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.
In March 2014 Finmeccanica announced its intention to sell AnsaldoBreda, saying the operating loss of the group had hit €227 million in 2013 against €160 million in the previous year.