New York's Department of Financial Services (DFS) said the scheme involved so-called mirror trades which illegally moved $10bn (£9.3bn) out of Russia.
DFS superintendent Maria Vullo said: "This Russian mirror-trading scheme occurred while the bank was on clear notice of serious and widespread compliance issues dating back a decade.
"It is obvious, though, that the scheme could have facilitated capital flight, tax evasion or other potentially illegal objectives."
The scheme involved wealthy clients buying stock in Moscow with rubles.
Then, shortly afterwards, related parties would sell the same stocks through the bank's London branch.
These trades, which were worth around $2m-$3m per order, were then cleared through Deutsche Bank's New York operation with the clients paying in dollars.
The DFS legal document which details the case says: "By converting rubles into dollars through security trades that had no discernible economic purpose, the scheme was a means for bad actors within a financial institution to achieve improper ends while evading compliance with applicable laws."
The New York regulator found the bank violated state banking law by conducting its business in an unsafe and unsound manner. It fined Deutsche Bank $425m (£397m).
The UK's Financial Conduct Authority (FCA) said it had issued a penalty of £163m - the largest of its kind in the UK - "for failing to maintain an adequate anti-money laundering (AML) control framework."
It accused Deutsche of exposing the UK's financial sector to the risk of financial crime.
Mark Steward, the FCA's director of enforcement, said: "The size of the fine reflects the seriousness of Deutsche Bank's failings.
"We have repeatedly told firms how to comply with our AML requirements and the failings of Deutsche Bank are simply unacceptable.
"Other firms should take notice of today's fine and look again at their own AML procedures to ensure they do not face similar action."
The matter is still being investigated by the US Justice Department and other regulators.
Deutsche, which is due to report its fourth-quarter results on Thursday, said it had already made sufficient provisions to cover the cost of the civil action.