A federal judge in Boston on Thursday approved an agreement by the British drug maker GlaxoSmithKline to pay $3 billion for criminal and civil violations involving 10 drugs, the largest health care fraud settlement in US history.

The amount of money involved led US District Judge Rya Zobel to remark that she was having trouble keeping track of the numbers.

GlaxoSmithKline pleaded guilty to promoting the popular antidepressants Paxil and Wellbutrin for unapproved uses.

Government officials said the company promoted Paxil as safe for children and adolescents, though the Food and Drug Administration had not approved it for those patients and the company’s clinical trials raised concerns about an increased suicide risk.

Prosecutors had charged the drug maker promoted Wellbutrin for unapproved uses that included treating attention deficit disorder, bipolar disorder, obesity, sexual dysfunction, and anxiety when it was not shown to be safe and effective for those uses.

The company also admitted it failed to report safety problems with Avandia.

In 2010, the diabetes drug was restricted in the United States and banned in Europe after it was found to sharply increase the risks of heart attacks and congestive heart failure.

Defense lawyer Geoffrey Hobart and Assistant US Attorney Sara Bloom declined to comment.

A GlaxoSmithKline spokesman referred to comments chief executive Andrew Witty made Monday, including that the company has learned ‘‘from the mistakes that were made.’’

When the government announced the settlement Monday, Deputy Attorney General James M. Cole called it historic, saying it sent a clear warning to any company that chooses to break the law.