Police said "high officials" of the British company had admitted the allegations under questioning after an investigation in the cities of Shanghai, Changsha and Zhengzhou.
Employees were said to have given free travel as "large bribes" to doctors, hospitals, foundations and medical associations in order "to open new sales channels and increase drug revenues", a statement from China's police ministry said.
It added: "After questioning, the suspects confessed to the crime."
A Foreign Office spokesman said: "We are aware of the Chinese investigation and we are providing consular assistance to a British national.
"We are in contact with GlaxoSmithKline and we are in the process of seeking further information from the Chinese authorities."
Glaxo said it was willing to co-operate with Chinese authorities but that the official statement was the first time it had been made aware of the nature of the allegations.
"However, if evidence of such activity is provided we will of course act swiftly on it."
Police in Changsha announced two weeks ago that Glaxo employees had been detained for questioning for unspecified "economic crimes". The company said at the time that it did not know what authorities were investigating.