Anyansi-Agwu had been with the club for 16 years, where he undertook various management roles.
The club boss will be remembered for his role in Enyimba's successes in the CAF Champions League, where they won the title in 2003 and 2004.
"Intense pressure from people who felt that I have stayed too long as well as consideration for my health are the reasons I felt the right time to throw in the towel is now after seeing the side win an unprecedented seventh league title," Anyansi-Agwu told SuperSport.
"The pressure on me to quit has been unprecedented despite quality results I have garnered within the period.
"I have given everything in me to see Enyimba succeed and if the place I come from has suddenly begin to hurt some people I think the sensible thing is to give way and allow some other people to come in and manage the team."