He called the move unprecedented, saying it was the first time a US institution had been driven out by a North Atlantic Treaty Organisation ally.
The university said it would retain "accreditation as a Hungarian university and ... continue teaching and research activity in Budapest as long as possible".
Ignatieff, who spent a turbulent three-year tenure as leader of Canada's federal opposition between 2008 and 2011, said the fate of CEU should serve as a warning sign to all democratic countries including Canada.
"CEU has been forced out", said CEU president and rector Michael Ignatieff, and the institution "couldn't wait any longer" to start its student recruitment for 2019.
"Despite our consternation at being forced to leave Budapest, we are excited to offer our students the opportunity to study in another great central European city", he said.
"The departure of these US -accredited programs from Hungary will be a loss for the CEU community, for the United States, and for Hungary", Nauert said.
In October, CEU warned it could be forced to move to Vienna, if it had not reached an agreement with the Hungarian government on Lex CEU (the moniker given to prime minister Orban's education reforms, widely seen as targeting CEU directly) before December 1.
Ignatieff said the Orban government imposed a host of new requirements for the university to meet in order to keep operating as an worldwide graduate school in Budapest.
Mr. Soros, who was born in Hungary and now lives in the United States, has been a frequent target for Mr. Orban whose vision for an "illiberal democracy" in Hungary clashes with the liberal, internationalist vision championed by Mr. Soros.
The government has called the university's decision to move to Vienna a "political bluff".
In 2017, Orban's then-chief of staff, Janos Lazar, said the education conflict was tied to Soros' advocacy for migration and refugees.
A university founded by the billionaire philanthropist George Soros says that it has been driven out of Budapest by a state-orchestrated campaign of "low tricks, propaganda and lies".
Budapest and Soros have also locked horns due to their contrasting stances on immigration, and the ruling Fidesz Party even accused him of attempting to meddle in the 2018 parliamentary election to favour pro-immigration candidates. In June, lawmakers approved the "Stop Soros" law, which allows criminal penalties of up to a year in prison for those convicted of aiding asylum-seekers.