Tweddell returned to Australia in 1988 as Managing Director of F. H. Faulding & Co, a pharmaceutical company based in Adelaide.
In 1999, Tweddell signed an agreement with the Federal Government where Faulding would receive $40 million in funding over five years in return for industry development.
The continued growth of Faulding led to Mayne Nickless buying the company leading to Tweddell's resignation as CEO and from the board in 2001.
In 1998, Tweddell was appointed as a director of the National Australia Bank, where he sat on a committee assessing business risk.
He resigned in 2004 after the foreign exchange scandal led to the bank losing hundreds of millions of dollars.