The board will make its recommendation for Richardson, currently the world cricket body's general manager, at the ICC annual conference in June, when Lorgat term ends.
The ICC nominations committee met in Mumbai at the weekend to interview four candidates for the role and obtained the ICC board's support today via teleconference for Richardson's nomination.
"It is a great honour to be nominated to be Chief Executive of the ICC. I am delighted with this opportunity and thank the ICC Board for their approval.
"It has been a privilege to serve as ICC General Manager