The bank, officially known as the Institute for Works of Religion (IOR in Italian) did not carry out enough checks on its clients and account holders were allowed to transfer large sums on behalf of others.
"There is a high risk that the way the IOR operates, without specifying its real clients, can be used as a screen to hide illegal operations," prosecutors wrote in a document that was quoted by Corriere della Sera.
They also faulted Italian banks that accepted transfers from the IOR for failing to probe the origin of the money, which is then moved into other banks.
"The IOR can easily become a channel for the laundering of money with a criminal origin, they said.
They also contradicted IOR statements that its account holders are all religious congregations or clergy.
"There are also private individuals who, because they enjoy a particular relationship with the Holy See, can deposit money and open accounts," they said.
The investigation centred on a €23 million ($30-million) transfer made from the Vatican bank to Italian lender Credito Artigiano in September 2010.
Three million euros were then sent on to Banca del Fucino and 20 million to JP Morgan Frankfurt.
The transfer was signed off by IOR's then director general Paolo Cipriani and his deputy Massimo Tulli, who both resigned last week.
Prosecutors are set to file charges against them.
La Repubblica said the two were also being accused over a dozen other smaller transfers to JP Morgan.
Pope Francis has set up a committee to investigate the bank and is said to be planning a major shake-up of the scandal-ridden institution as part of broader reforms of the Vatican bureaucracy.
The Vatican is reforming its finances in order to be included on a "white list" of states that respect international rules against money laundering.
Italian police last month arrested a senior cleric on suspicion of money laundering and fraud for allegedly plotting to smuggle millions of euros into Italy.