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.
"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.
Patterson, who has led BT since 2013, announced plans last month to cut 13,000 jobs as part of a restructuring created to simplify the group's management structure.
The move comes nearly a month after BT revealed plans to reduce its workforce by about 13,000 jobs over the next three years, with mainly back office and middle management roles set to be cut, with the telecommunications giant hoping to "drive sustainable long term growth in value for shareholders".
Following the news of Mr Patterson's departure, BT's shares jumped 3% initially, before dropping back to trade at about 202p.
Last month, the company announced an ambitious restructuring.
He was "immensely proud" of what had been achieved at the former telecoms monopoly, in sports broadcasting, mobile and a hard-won agreement with the regulator to keep hold of its networks business Openreach. He had missed out on a bonus in the previous year after a number of setbacks.
Investors in BT Group Plc watched their investments shrink about 60 percent and decided it was enough.
That strategy update was released alongside full-year results which showed a 1% drop in revenue to £23.7 billion, through reported pre-tax profits rose 11% to £2.6 billion.
"I am confident that, for the remainder of his term, Gavin and his senior management team will continue to display the energy required to deal with every dimension of the task at hand", he said.