By Dylan Tokar and Micah Maidenberg

Novartis AG and a former subsidiary of the Swiss drugmaker agreed to pay a combined $347 million to resolve allegations that the companies ran schemes to bribe public hospitals and clinics in Greece, Vietnam and South Korea, U.S. authorities said Thursday.

The settlements with Novartis and its former eye-care unit, Alcon Inc., bring to a close investigations by the U.S. Department of Justice and U.S. Securities and Exchange Commission into alleged criminal and civil violations of the Foreign Corrupt Practices Act.

The settlements with Novartis represent the second time the drugmaker has been fined for alleged foreign bribery-related offenses.

The Novartis and Alcon subsidiaries involved in the misconduct entered into deferred prosecution agreements with the Justice Department to resolve the criminal charges, which were filed in the U.S. District Court in New Jersey.

Novartis's parent company entered into a separate agreement with the SEC to resolve the regulator's civil claims, which also covered allegations that the company and its former subsidiary used forged contracts as part of financing arrangements in China that led to the writing off of more than $50 million in bad debt.

The latest investigations into Novartis by U.S. authorities began in 2016, according to Novartis. Greek prosecutors in 2018 sent a report to parliament alleging that Novartis employees had paid tens of millions of euros in bribes to doctors and politicians to fix the price of its drugs at artificially high prices.

Novartis has long denied some of those claims. "Today's resolutions contain no allegations relating to any bribery of Greek politicians, which is consistent with what Novartis found in its own internal investigation," the company said in a statement.

Alcon, which merged with Novartis in 2011 and was spun off from the firm last year, said it was pleased to resolve the investigations.

The agreements announced Thursday detailed a scheme by the Novartis subsidiary, based in Greece, to bribe employees of Greek state-owned and state-controlled hospitals and clinics by sponsoring their travel to international medical conferences, including events held in the U.S.

What the subsidiary wanted in return was clear, prosecutors said. According to the agreement, the Novartis unit expected the publicly employed health-care workers to increase the number of prescriptions they wrote for Lucentis, a medication used to treat certain eye conditions.

In one instance, an internal action plan directed employees to convey to an unidentified Greek health-care provider that "to get you must write. No presents anymore." The scheme lasted from 2012 to 2015, prosecutors said.

The Novartis subsidiary also admitted in its settlement with prosecutors to paying bribes between 2009 and 2010 to health-care providers in connection with an epidemiological study aimed at increasing the sales of Novartis-branded drugs.

The bribery schemes constituted a conspiracy to violate the FCPA, according to prosecutors. In attempting to hide the schemes, the Greek subsidiary also caused Novartis to record false books and records, in what constituted a second conspiracy to violate the antibribery statute, prosecutors said.

The Novartis business for Greece agreed to pay a criminal penalty of $225 million, while its parent company agreed to pay more than $112 million in disgorgement and interest, representing the amount of illicit profits.

The Alcon subsidiary, meanwhile, also conspired to violate the FCPA by creating false books and records to hide alleged bribery schemes and other misconduct, according to the Justice Department and the SEC.

The false books and records resulted in part from a scheme that took place between 2011 to 2014 in which Alcon employees in Vietnam paid bribes through a third-party distributor to employees of state-owned and state-controlled hospitals and clinics in the southeast Asian country, prosecutors said.

The scheme was intended to increase the sale of artificial lenses used to treat cataracts and other ailments. The distributor was reimbursed for up to 50% of the cost of the corrupt payments, which were recorded as consulting, marketing and human resource expenses, among other things.

The Alcon subsidiary will pay a criminal penalty of about $8.9 million, the Justice Department said.

Both companies have agreed to enhance their compliance programs and file reports on their efforts, authorities said.

Novartis in 2016 agreed to pay $25 million to settle claims by the SEC that it violated the FCPA by engaging in pay-to-prescribe schemes in China. The company at the time neither admitted nor denied the regulator's allegations.

It also faced criminal charges in 2015 over a strategy of inducing specialty pharmacies in the U.S. to boost sales of Novartis drugs by paying kickbacks in the form of rebates.

"With today's agreements, all outstanding FCPA investigations into Novartis are now closed," the Swiss company said.

Write to Dylan Tokar at dylan.tokar@wsj.com and Micah Maidenberg at micah.maidenberg@wsj.com

Corrections & Amplifications

This story was corrected at 11:08 p.m. EST. The original incorrectly said Novartis AG faced criminal charges in 2018 over rebates it paid to pharmacies. It was in 2015.