"As I look ahead, I see that the current disruption is simply putting too much unnecessary pressure on the business, our over 200,000 people and their 500,000 or so dependents, and the clients we serve in 112 countries", he said.
Sorrell will be available to assist with the transition.
Chairman Roberto Quarta will become executive chairman until a new chief executive is found, while Mark Read, a WPP digital executive, and Andrew Scott, chief operating officer, Europe, have been appointed as joint chief operating officers.
"However, I believe it is in the best interests of the business if I step down now", he said.
Sorrell's exit caps a remarkable turnaround for the 73-year-old, whose iron grip on WPP helped characterise its rise into the world's largest advertising company.
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"Obviously I am sad to leave WPP after 33 years", Sorrell said in a statement.
However, his departure will leave the company he built virtually from scratch facing profound questions about its future direction.
Sorrell had denied allegations of misuse of company funds and improper personal behaviour, according to British media reports.
"During this time, the company has been successful because it has valued and nurtured outstanding talent at every level - within and well beyond our leadership teams", he said.
Born in London, Sorrell studied economics at the University of Cambridge and then gained a masters from Harvard University.
WPP, then Wire and Plastic Products, was a United Kingdom manufacturer of wire baskets for the first 14 years of its life until 1985 when Sir Martin took a loan out against shares he owned in Saatchi & Saatchi and purchased a stake in the company after seeking a public entity through which he could build a marketing company.
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Some multinational advertisers, including P&G, which owns Ariel and Gillette, have signalled their intention to take more of their marketing services activity in-house, reducing the lucrative work for which they are charged by external agencies.
The longest-serving CEO on the FTSE 100 blue chip index, Sorrell built WPP into one of Britain's biggest companies by three decades of relentless dealmaking.
Sir Martin said his position at WPP had been a passion for so long but it was in "the best interests of the business" for him to resign.
There can be little doubt WPP has made Sir Martin a wealthy man - the Sunday Times Rich List in 2017 suggested a figure of £495 million - but he would frequently come in to bat against those who deemed his pay deals excessive.
The resignation brings an abrupt end to the 33-year reign of Sorrell, during which he transformed a small shopping basket manufacturer into a global advertising powerhouse.
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