60-year-old Wilkinson, a former English Football Association technical director, has signed an open contract, China's Xinhua news agency reported.
"During the next three years, Wilkinson will try to establish Shenhua as a first-class team in Asia," the club was quoted as saying.
Shenhua have been without a coach after Wu Jingui resigned to become the assistant of Chinese national coach Arie Haan of the Netherlands.
Wilkinson had reportedly turned the Shenhua job down earlier this month and on Friday was named as first choice by the Egyptian Football Association's general secretary to take over their national side.
In his first full season at Elland Road, Leeds won the Second Division championship. Our first season back in the First Division, we finished fourth and the following year we won the First Division championship.