Knapp, who has been with the company for ten years, is believed to be leaving with a £1.3 million pay-off. He will relinquish his responsibilities on Friday, but will stay with the company until the end of the year as a strategic adviser.
Since founding ntl in 1993, Knapp has turned it into the UK's largest cable-TV operator. However, the past few years have been turbulent. With debts in excess of £12 billion, ntl embarked on a financial restructure at the end of last year, having also filed for Chapter 11 bankruptcy status.
It emerged from this in January, after converting £7 billion of debt into equity and splitting the company into two divisions: ntl UK and Ireland and ntl Europe.
Knapp's resignation came as the company announced a second-quarter pre-tax loss of £153 million, which is down from a loss of £267 million last year. Its revenue has risen year on year to £551.3 million from £549 million.
These positive results, plus the improvement in the company's New York listed share price, were enough to persuade Knapp that his mission at ntl had been completed.
His replacement, Duffy, joined ntl in April as one of several senior appointments. James Mooney was made the non-executive chairman and Scott Schubert became the chief financial officer.
Duffy was previously the finance chief at Orange, which is owned by France Telecom. France Telecom holds a 25 per cent stake in ntl.
His decision to join ntl followed his unsuccessful bid to become Orange's chief executive. That position went to Solomon Trujillo.
Under Duffy, ntl is expected to merge with its rival Telewest, which is restructuring in an effort to deal with its own financial problems.
A merger would create a credible pay-TV rival to BSkyB.