LONDON-- GlaxoSmithKline PLC on Thursday named Philip Hampton as its next chairman, a move that while expected comes as the pharmaceuticals giant struggles to right itself amid a series of probes over alleged overseas bribery.

Mr. Hampton, currently chairman of Royal Bank of Scotland Group PLC, will succeed longtime Glaxo Chairman Christopher Gent. Glaxo said Mr. Hampton would join its board as a nonexecutive on Jan. 1 and become deputy chairman from April 1 before replacing Mr. Gent on Sept. 1 next year, or earlier if he is released from his other commitments.

Mr. Hampton will leave RBS at some point during 2015 after the 80% U.K. state-owned bank finds a suitable successor, the bank said in a separate statement.

Mr. Gent had previously been slated to step down by the end of next year and told shareholders earlier this year that he hoped that his successor would be named by the end of this year. Mr. Gent has served as chairman for almost a decade.

Mr. Gent had been under increasing pressure this year amid a series of probes into Glaxo's global practices.

Last week, a Chinese court found the drug maker's local subsidiary guilty of bribery and fined the company nearly $500 million.

Separately, Glaxo has been investigating claims its employees bribed doctors in Iraq, Jordan, Lebanon and Syria. Glaxo has apologized for the Chinese bribery and said it cooperated fully with investigators. It has said it takes all of the other allegations seriously, as its investigations continue.

The company also cut its full-year earnings forecast in July, after weak U.S. sales and currency moves hit second-quarter net profit. This year, shares have fallen 11%, even as those of its European rivals have gained ground.

Mr. Hampton joined RBS in January 2009 soon after its GBP45.5 billion ($74.3 billion) government bailout. During his tenure, the former Lazard banker played a crucial role negotiating with the U.K. treasury over issues including the shape of the bank and how much it should pay its chief executive.

But the 60-year-old executive never achieved his initial aim: to steward the bank back into private hands. Mr. Hampton has said that he thought he would stay in as RBS chair for between five and seven years. It is unclear who will succeed him.

Previous to his post at RBS, Mr. Hampton was the chairman at supermarket group J Sainsbury PLC.

At Glaxo, Mr. Hampton will be paid GBP85,000 ($138,900) a year as a nonexecutive director, GBP350,000 when he becomes deputy chairman, and GBP700,000 on his appointment as chairman. His salary will be paid in cash and shares.

Write to Max Colchester at max.colchester@wsj.com and Hester Plumridge at Hester.Plumridge@wsj.com

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