Ernst von Freyberg, president of the IOR, will work with bank management to finalize changes that fulfill the Vatican's new financial structures, the statement said.
The pope identified the bank as a key target of reforms after his election last year and had not ruled out its closure if it was unable to conform to international standards of transparency and accountability.
Last year the bank published details of its accounts for the first time, and a team of experts from the Promontory Financial Group, a regulatory compliance consulting firm, began screening the 19,000 accounts held by the bank, looking for signs of money laundering and other crimes.
The Vatican bank has struggled to clean up its image since Roberto Calvi, dubbed "God's banker" because of his dealings with it, was found hanging beneath Blackfriars Bridge in London in 1982 in a suspected Mafia killing.
More recently the bank's former president, Ettore Gotti Tedeschi, was sacked in 2012 after Italian prosecutors seized 23 million euros ($29 million) from a Rome bank account registered to the IOR amid suspicions of money laundering.
Now Monsignor Nunzio Scarano, a former Vatican accountant with close links to the IOR, faces a trial on charges of money laundering and allegedly plotting to smuggle millions of dollars from Switzerland into Italy in a tax-dodging scheme.
Paolo Cipriani and Massimo Tulli, the former director and deputy director at IOR, who resigned in July after Scarano's arrest, have also been ordered to stand trial on charges of violating anti-money-laundering norms.
The pope's approval "represents for us a strong accreditation, a great recognition of the importance of our mission and service work done in the last 12 months," IOR spokesman Max Hohenberg said in a statement.