The 32-year-old has been under the spotlight since his coach Alberto Salazar was accused of violating anti-doping rules in a BBC documentary earlier this month.
This week Britain's Daily Mail reported that Farah had missed two out-of-competition doping tests in 2010 and 2011.
At the time, the rules meant that a third missed test within an 18-month period (now reduced to 12) would almost certainly have resulted in a ban that would have probably ruled him out of the London 2012 Olympic Games, where he won gold in the 5,000 and 10,000 metres.
"I have never taken performance-enhancing drugs in my life and I never will," Farah said in a statement published on his Facebook page on Friday.
"Over the course of my career I have taken hundreds of drugs tests and every single one has been negative.
"I've fully explained the only two tests in my career that I have ever missed, which the authorities understood, and there was never any suggestion that these were anything more than simple mistakes."
American Salazar, who has worked as a consultant for British Athletics since 2013, has denied the allegations, saying the BBC and US website ProPublica had engaged in "inaccurate and unfounded journalism".
Farah, who was not accused of any wrongdoing in the BBC documentary, withdrew from a Diamond League meeting in Birmingham earlier this month after expressing anger over the allegations made about Salazar.
Farah was upset his name had "been dragged through the mud" and said he would seek assurances from Salazar, with whom he has worked since 2011.
"As I made clear, I went to Portland to speak to Alberto Salazar and demand answers," Farah said.
"He reassured me that the claims are false and that he will soon be providing evidence to make that clear. Until then I will not be commenting further on the allegations."
UK Athletics are currently conducting a formal review into the relationship between Salazar and Farah, which is expected to be completed by the first week in August.
Farah announced on Wednesday he will return to competitive action at the Monaco Diamond League meeting on July 17.
Image: Mo Farah of Great Britain.
Photograph: Ben Hoskins/Getty Images