Before taking over as head coach, former Warwickshire batsman Moles had been working as Afghanistan's batting coach, a position he was only appointed to in June this year.
His first assignment with the Afghanistan side will be on the tour to Australia and New Zealand, for eight fixtures designed to prepare the side for the World Cup next year. The tour begins on September 12, and will see Afghanistan play eight fixtures against state and district sides, although their attempts to organise a one-day international against Australia or New Zealand were turned down.
"The good thing about Andy is that he's worked with a full member team - New Zealand," the Afghan Cricket Board CEO Noor Mohammad Murad told ESPNcricinfo. "And the World Cup will also be held in New Zealand. A 100% focus is on the World Cup."
Since retiring as a player in 1997, Moles has enjoyed a diverse coaching career. He has worked for Griqualand West, Northern Districts and New Zealand, who he coached for a year from 2008. Moles also has a proven pedigree with associate sides, and led Scotland to victory in the ICC Trophy in 2005, earning them qualification for the 2007 World Cup.
His appointment brings to an end Khan's six-year involvement in Afghan Cricket, although he may yet work in an advisory capacity. Khan worked as head coach from 2008 to 2010, before resigning citing board interference with the team during a tour of Scotland.
He returned to Afghanistan at the end of 2011, and oversaw a run of six consecutive World Cricket League victories that resulted in qualification for the 2015 World Cup last October.
ESPNcricinfo understands that Khan originally tried to resign six months ago, but the Afghan Board has only now accepted his resignation because Moles is an obvious successor. Khan's contract had been due to expire at the end of the year but he has stood down now citing "personal issues and commitment with his family", Murad said. "We respect his decision.
"Some media outlets have described Kabir Khan's resignation as a setback and a major blow for Afghanistan cricket. We do not see it this way. We see it as a new opportunity for further development both of the national team and our national cricket generally.
"Whilst Kabir shared his particular skills with our players over a long period, Andy Moles brings different skills. He comes to us at this important time with a wealth of experience in international cricket both as player and coach."
The Afghan Cricket Board have also confirmed that Peter Anderson, the former South Australia and Queensland wicket-keeper and current coach of the Afghanistan National Cricket Academy, will accompany the side on their tour of Australia and New Zealand.