Patterson, who has led BT for almost five years, announced 13,000 job cuts last month in an attempt to address multiple pressures on the business.
But a failure to hit a revenue target and a forecast for flat profits for the next couple of years sent its shares down to near six-year lows.
"The broader reaction to our recent results announcement has ... demonstrated to Gavin and me that there is a need for a change of leadership to deliver this strategy," he said.
A search for Patterson's successor has started, the company said, and it expects to have a successor in place during the second half of the year.
BT shares rose more than 2 percent in early trading.
Patterson said he was "immensely proud" of what had been achieved at the former telecoms monopoly, including a multi-billion pound move into sports broadcasting, buying Britain's biggest mobile operator EE and a hard-won agreement to create greater independence for its networks business Openreach.
But the admission that fraud had left a 530-million pound black hole in its Italian business, combined with sharp slowdown in demand from public sector and corporate customers, forced the 50-year-old executive to cut profit targets in 2017.
At the same time, Patterson was embroiled in fractious talks with Britain's telecoms regulator Ofcom about the fate of Openreach, which runs the national broadband network.
Patterson said 15 months ago that BT had been taken aback by the flak it had received about the company's customer service and its networks, and he vowed that its millions of customers would see improvements.
However, the decline in the company's shares continued, and a plan announced last month to save 1.5 billion pounds a year by 2020/21 failed to impress investors, putting Patterson under ever increasing pressure.
(Reporting by Paul Sandle; Editing by Guy Faulconbridge and Mark Potter)
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)