The Japanese conglomerate could spend as much as 1.25 billion euros to become the sole owner of Ansaldo STS, which it said would have a leading role to play in growing its rail business, including through acquisitions.
Hitachi and investment funds led by Elliott have been rowing since the Japanese company took a majority stake in Ansaldo STS in 2015, with Elliott - which holds a minority stake - complaining about the price paid by Hitachi as well as Ansaldo's strategy and governance.
Under the deal announced on Monday, Hitachi will pay a premium of 9.5 percent to buy Elliott's 31.79 percent stake in Ansaldo STS, costing it around 807.6 million euros ($920 million).
It will then launch a bid for the rest of Italian company with the aim of delisting it.
Hitachi will buy Elliott's shares in Ansaldo STS at 12.70 euros. The mandatory bid on residual shares will then be launched at the same price.
Ansaldo STS shares rose more than 9 percent to a session high of 12.68 euros, matching the offer price.
Owned by U.S. hedge fund manager Paul Singer, Elliott is an outspoken investor in many European and U.S. companies.
In 2015 Elliott refused to sell its Ansaldo STS shares to Hitachi in a previous public offer on the Italian company, judging the 9.50 euro per share price offered then too low.
The railway industry was shaken last year when Alstom and Siemens announced a plan to merge their rail units into a Franco-German champion to stave off competition from bigger Chinese rival China Railway Rolling Stock Corporation and Canada's Bombardier Transportation.
($1 = 0.8776 euros)
(Reporting by Francesca Landini, writing by Giulio Piovaccari, editing by Stephen Jewkes; Editing by Giulia Segreti, Edmund Blair and Kirsten Donovan)