The settlement, originally announced in December, is the largest penalty imposed on a bank.
The US Justice Department's case maintained that HSBC's failure to monitor itself allowed criminals and suspect countries such as Cuba, Burma and Sudan to move hundreds of millions in prohibited transactions through US financial institutions from the mid-1990s to 2006.
Judge John Gleeson of the US District Court for New York's Eastern District approved the plan, which requires court supervision of HSBC for five years, after which the US will seek to dismiss the case.
Separately, Standard & Poor's Ratings Services has lowered the long-term counter-party credit ratings of Barclays Bank, Credit Suisse and Deutsche Bank to A' from A-plus.
The agency kept its A/A-1 long and short-term ratings on Switzerland's UBS.
"We see increasing risks for some large Europe-based banks operating in investment banking, as regulators and uncertain market conditions make operating in the industry more difficult," S&P said.
In particular, these banks' debt-holders face higher credit risks because of tighter regulation, fragile global markets, stagnant European economies, and rising risk of financial crisis-related lawsuits.
S&P said Barclays, Credit Suisse, Deutsche Bank, and UBS were "among the most exposed in Europe" to global regulatory changes.