Osinbajo said the huge sum was “lost... to fraudulent and corrupt practices in... security equipment spending during the last administration”, according to a statement released by his office on Tuesday.
The figure is more than half of Nigeria's current foreign exchange reserves of $27 billion, he said on Monday in a speech in the southwestern city of Ibadan.
President Muhammadu Buhari took office in May last year vowing to crack down on endemic corruption and impunity in government and has set about bringing offenders to book.
The most high-profile figure arrested and charged so far is Sambo Dasuki, who was national security advisor under Buhari's predecessor, Goodluck Jonathan.
Dasuki is accused of diverting money earmarked for military procurement to fund Jonathan's presidential election campaign, in bogus arms deals totalling billions of dollars.
Former chief of defence staff Alex Badeh is also on trial, accused of fraudulently diverting $19.8 million from salaries meant for service personnel for his own use.
Buhari has previously complained that Jonathan's administration left government coffers “virtually empty”, worsening economic difficulties caused by a slump in global oil prices.
Information Minister Lai Mohammed said in January that just 55 people stole some $6.7 billion in public funds between 2006 and 2013.
Buhari, a former army general and military ruler, has vowed to recover “mind-boggling” sums of cash stolen by the corrupt elite over decades.
Osinbajo said there would be consequences for the corrupt and that “no public officer can steal the resources of this country and expect to escape”.
Instead of shamelessly stealing public funds with impunity, Nigeria's elite needed to set an example.
“Society fails when the elite abdicates its role,” the vice-president added.