The grocer said yesterday that Pennycook had informed the board he would concentrate on building “a portfolio career”.
“I feel that it’s the right time to seek new challenges,” he said in a statement.
Chairman Ian Gibson said Pennycook had done “an outstanding job” for the firm.
Last month Morrisons posted a one per cent fall in first quarter sales, while earlier this month its former executive chairman Ken Morrison expressed concern at its annual shareholders meeting at recent developments at the grocer.
After failing to win the job of chief exec two years ago, Pennycook, 48, received a package entitling him to receive 456,000 shares, worth £1.25m at the grant date, as long as he was still with the company in March 2013, and the company’s earnings per share growth matched inflation. He received £1.12m overall last year.