Ma will continue as executive chairman of the company over the next 12 months to ensure a smooth transition.
Then Ma will finish his run on the Alibaba Group's board of directors after its annual shareholder meeting in 2020.
Ma, a former English teacher, founded Alibaba in 1999 in an apartment in the eastern city of Hangzhou to connect Chinese suppliers with foreign retailers.
Mr. Zhang had previously served as Taobao's chief financial officer, president of Tmall.com and as Alibaba's chief operating officer before succeeding Jonathan Lu as chief executive.
Zhang will also retain the CEO title, the company said.
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He is also known for his eccentric personality and has donned wigs and costumes to perform highly choreographed pop routines at company events.
The report of his retirement came as a surprise, especially in the Chinese government circles as the NYT report said Mr. Ma was relinquishing as China's business environment had soured, with the government and state-owned enterprises increasingly playing more interventionist roles with companies.
Ma, who turned 54 on Monday, will continue to mentor senior management as part of an advisory board called the "Alibaba Partnership". Mr Ma has lately taken on educational initiatives as a pet project. He has also established a scholarship program in Newcastle, Australia.
Alibaba maintained robust revenue growth in the first half of 2018, but its profit margins have been squeezed by big-ticket investments as it battles to maintain pole position in payments and e-commerce.
The company, which is battling arch rival Tencent Holdings for pole position in the food delivery market, recently said it will merge units including Ele.me and Koubei and raise funds for the combined business.