President Uhuru Kenyatta divulged the news on Tuesday afternoon and thanked Mr Muigai for his service for the last six and a half years.
The Head of State mentioned that he had nominated Judge Paul Kihara Kariuki to replace Prof Muigai.
"I have received with regret the resignation of Attorney General Prof. Githu Muigai. I thank him for his service for the last six and a half years. I have nominated as his replacement Judge Paul Kihara Kariuki," President Kenyatta tweeted.
At the same time, Mr Kenyatta nominated Patrick Gichohi (Commissioner of the Public Service Commission), Prof Olive Mugenda (former Kenyatta University Vice Chancellor) and Felix Koskei (former Agriculture Cabinet Secretary) to the Judiciary Service Commission.