Mukhtar Ablyazov's wife Alma Shalabayeva and their daughter Alua were bundled into a plane and deported to Kazakhstan last year in a hugely controversial move by Italy's interior ministry that is under investigation. The little girl was just six years old at the time.
They returned in December 2013 after being given new Italian visas allowing them to leave Kazakhstan following a political furore over their treatment.
Their lawyer Anton Giulio Lana said the government now recognised Shalabayeva's "founded fear of persecution." The family had lived in Rome before the deportation.
A former Kazakh energy and trade minister, Ablyazov is accused of having stolen billions of dollars in state and investor funds while leading the Kazakh BTA Bank, which also had interests in Russia and Ukraine.
Ablyazov became an opposition figure after being arrested over the fraud charges in 2002. He then fled Kazakhstan for Britain, saying that the accusations against him were politically motivated.
His refugee status in Britain has since been revoked.