"Whoever dares to spurn the state's laws and commit such outrages will be harshly punished by party rules and national law," the paper said.
It added that Zheng's demise "fully expressed the party's and state's unwaveringly staunch commitment to stamping out corruption".
"Whoever dares to spurn the state's laws and commit such outrages will be harshly punished by party rules and national law"
The execution comes as Hu Jintao, China's president, prepares for a party congress later this year that is set to extend his tenure as party chief.
Hu has staked his leadership on the promotion of tough but clean and corruption-free government.
According to official reports Zheng's receipt of kickbacks in return for favours went back a decade before he was finally exposed.
From 1997, Zheng used his grip on drug approval powers to squeeze bribes that went to his wife and son, the officials Xinhua news agency said.
In one case a company in Zhejiang province in the east fed "consultancy fees" and other rewards worth almost $400,000 to them, the report said.
Later, beginning in 2001, Zheng used a shake-up of drug approval rules to concentrate power with him and some close associates.
Under Zheng's watch several companies - including some investigated for using fake ingredients - were allowed to register substandard medicines in return for a bribe, Xinhua said.
Zheng's execution marked the first time China has imposed a death sentence on an official of his rank since 2000.
It comes against a backdrop of growing domestic and international concerns over the safety of Chinese-made goods, following a series of health alerts over food, drugs and other products.
On Tuesday the SFDA, the watchdog body that Zheng once headed, pledged to step up efforts to improve safety standards acknowledging that such efforts in the past was "not very satisfactory".