Teasdale, the current chairman of both Business in Sport and Leisure (BISL) and the Institute of Groundsmanship (IOG), had been acting as a consultant for the sport.
He replaces the acting chair, David King, who led the panel that conducted a lengthy and rigorous recruitment process.
That group included Liz Nicholl, chief executive officer of UK Sport.
King welcomed the appointment.
"Mr Teasdale has had a successful career in business, as well as impressive credentials in sport and government in this country," he said.
"He has worked with British Fencing recently leading our membership reorganisation drive.
"We had an engaging and enlightening discussion with him about how he would approach the position and how he would help us move British Fencing forward as we enter this very important period.
"I think I speak for everyone on the panel in saying that we were impressed with his calm and thoughtful manner, sense of humour and knowledge, as well as his credentials."
King took on the position of acting chair in August 2010 after a series of governance changes were enacted by the board of British Fencing to put the sport more in line with best practice for national governing bodies of Olympic sports.
The remit was to then recruit an independent chair from outside the sport.
Teasdale was chairman of Goodform Limited, a specialist marketing agency whose clients included the Football Assocation, the Rugby Football Union, England and Wales Cricket Board, the Amateur Swimming Association, England Squash, Sport England, UK Sport and the Central Council of Physical Recreation.
He has also previously worked as the interim chief executive of Badminton England.
"Fencing is a great traditional sport, with enduring values, appeal to young and old and real potential for growth," said Teasdale.
"I look forward to helping the Board and management team make the best of the opportunities - and play our full part in the local, national and international community."