Flanigan and Moore will not be directly replaced.
A TMG spokesman said: "The restructure will allow for a decentralized digital strategy going forward and the changes implemented will streamline operations to align digital and marketing activity more closely with the commercially focused areas of the business.
"In light of the current challenging economic environment, and the likelihood that conditions will toughen in 2009, the restructure will strengthen our ability to meet the challenges ahead."
Flanigan joined TMG in January this year after leaving his role as director of marketing and communications at AOL UK. He replaced Katie Vanneck who returned to The Times as sales and marketing director.
Moore was promoted to general manager of digital from his role as executive director of consumer markets in May this year. He also joined TMG from AOL in late 2007.
Separately, TMG has appointed Lorraine Twohill, Google's vice president of marketing for Europe, the Middle East and Africa to the board as non-executive director with immediate effect.
Twohill has worked at Google for more than years and is responsible for the Google brand and all of Google's regional marketing activities throughout EMEA.
Before joining Google in 2003, initially as director of product marketing, she was the European head of marketing for online travel company Opodo from 2001 to 2003.
Murdoch MacLennan, chief executive of Telegraph Media Group, said: "Lorraine's blend of digital, marketing and commercial experience will be of immense value as we continue to develop our multi-media strategy."
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