Armstrong, who was stripped of his seven Tour de France titles from 1999-2005 in October, received £300,000 from the Sunday Times as payment towards his legal fees after the paper raised questions about the American's success following his recovery from testicular cancer.
"It is clear that the proceedings were baseless and fraudulent. Your representations that you had never taken performance enhancing drugs were deliberately false," read the letter to Armstrong's lawyers in the Sunday Times.
The paper is demanding the return of the £300,000 payment plus interest, as well as costs accrued in defending the case, which was settled in 2006.
A report by the United States Anti-Doping Agency in October said the now-retired Armstrong had been involved in the "most sophisticated, professionalised and successful doping program the sport has ever seen."
Armstrong has always denied using performance-enhancing drugs but chose not to contest the USADA charges.