The former prominent newspaper editor is the most high profile figure to be named in what is being called India's #MeToo movement.
The charges range from "predatory behaviour" to sexual assault.
Mr Akbar had earlier filed a criminal defamation case against the female journalist who first named him.
He said in a statement that since he had decided to challenge the "false accusations" against him in his "personal capacity", he felt it was appropriate to step down from office.
Mr Akbar's resignation came as pressure grew on the government to respond to the allegations being made against him.
One of India's most influential editors, he has edited leading English-language newspapers in India, such as The Telegraph and The Asian Age.
He was first named last week by journalist Priya Ramani, who retweeted an article she had written for Vogue India a year ago titled "To the Harvey Weinsteins of the world", where she recounted what she called her first experience of workplace harassment.