Deutche Bank AG has agreed to pay nearly $630 million to end probes by U.K. and New York regulators into Russian equity trades that transferred $10 billion out of that country in violation of anti-money-laundering laws.

The two fines--$204 million to the U.K.'s Financial Conduct Authority and $425 million to New York's Department of Financial Services--partially end a big legal question that has been hanging over the German lender. The settlement doesn't end a separate ongoing probe by the U.S. Justice Department. It is unclear when a potential settlement in that investigation might be reached.

Deutsche Bank said the $630 million in settlements announced Monday and Tuesday are "already materially reflected" in existing litigation reserves and that it is cooperating in ongoing probes into the Russia trades.

Earlier this month, Deutsche Bank separately agreed with the U.S. Justice Department to pay $7.2 billion in cash and consumer relief to end a series of mortgage-securities probes. The $3.1 billion cash portion was seen by analysts and investors as a manageable outcome, and ended speculation that the anticipated settlement might force the bank to immediately raise capital.

Investors' attention remains on the bank's mounting legal costs heading into its fourth-quarter earnings report, scheduled Thursday.

U.K. authorities said Tuesday that its fine related to the Russian trades is the largest it or its predecessor regulator has imposed for failings in anti-money-laundering controls.

The U.K. and New York regulators cited repeated shortcomings in Deutsche Bank's controls to vet clients and detect suspicious trades. The lender executed more than 2,400 pairs of so-called "mirror trades" between April 2012 and October 2014 alone, the U.K. regulators said.

The trades allowed customers to transfer billions of dollars out of Russia to banks in Cyprus, Estonia and Latvia, U.K. authorities said. Deutsche Bank's Moscow office handled both sides of the trades simultaneously, converting rubles into dollars and moving the funds out of Russia.

The U.K. authorities said the transfers were "highly suggestive of financial crime."

Regulators said Deutsche Bank cooperated in the probes and has made improvements to its anti-money-laundering program and other controls. The bank agreed with New York authorities to bring in an independent monitor for up to two years as part of that settlement.

The trades in question involved Deutsche Bank offices in Moscow, London and New York between 2011 and 2015.

The New York regulator said the average size of relevant orders was between $2 million and $3 million. Traders were able to bypass Deutsche Bank's compliance rules, the regulator said.

"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," according to the consent order between Deutsche Bank and the New York regulator.

Write to Jenny Strasburg at jenny.strasburg@wsj.com