The sum, which needs final approval, is far lower than the $14bn the US had asked the bank to pay in September, the BBC reports.
That looming fine had caused concerns that a failure of the bank could pose a risk to the global financial system.
Credit Suisse also announced a similar deal, while Barclays is now under investigation too.
The sale of residential mortgage-backed securities played a significant role in the 2008 financial crisis.
Several banks in the US have been subject to investigations over allegations of giving mortgages to unqualified borrowers, then repackaging those loans as safe investments and selling the risk on to others. The inquiries related to deals done between 2005 and 2007.
Meanwhile, Credit Suisse has said it has agreed a $5.28bn deal to settle its own dispute with US authorities over mortgage-backed securities.
The Swiss bank will pay US authorities $2.48bn, and will also give consumers $2.8bn in compensation over the next five years.
Press say Deutsche Bank fine ‘could have been worse’
German commentators note that the Deutsche Bank management will be relieved that the fine agreed with US regulators is only about half of what was originally demanded, but that $7.2bn is still a lot of money to pay.
Tobias Kaiser writes in Die Welt that the deal “will generate a sigh of relief at Deutsche Bank headquarters… But the punishment that has now been agreed on is still a hefty one.”
The business daily Handelsblatt says: “Though it is no longer expected to pay the sum demanded at the outset, the financial institution must still dig deep in its coffers.”
Claus Hulverscheidt, writing in Suddeutsche Zeitung, agrees: “It could have been even worse for Deutsche Bank, but the punishment that has now been agreed with the US Department of Justice will put a heavy burden on the country’s biggest financial institution for years to come.”
At the same time, the US Department of Justice has said it is now also suing Barclays for alleged mortgage securities fraud.
It alleged that from 2005 to 2007, Barclays “repeatedly misrepresented the characteristics of the loans backing securities they sold to investors throughout the world, who incurred billions of dollars in losses”.
Other banks
Deutsche Bank operates in 70 countries with 100,000 employees, but is shedding about 15 per cent of its workforce, disposing of its retail bank, Postbank, and pulling out of other countries.
Its assets are about €1.6tn. HSBC, the biggest non-Chinese bank in the world, has assets 50 per cent greater than that, but Deutsche is still in, or near, the top 10 biggest global banks.
Under the settlement, Deutsche’s payment will be made up of a civil penalty of $3.1bn, as well as $4.1bn in consumer relief that will help US homeowners.
Other banks that have been ordered to pay fines by the US Department of Justice include Citigroup, which says its $12bn penalty has been reduced to $7bn.
In 2013, JP Morgan Chase was fined $13bn, following allegations that it overstated the quality of mortgages being sold to investors. In the following year, Bank of America paid $16.7bn to settle similar charges.
Goldman Sachs settled for $5.1bn in January this year.
