Snedden, who played 25 Tests and 93 ODIs between 1980 and 1990, has played prominent roles at NZC in the past too - as chief executive and a board member of the organisation from 1990 to 1992; 1999 to 2001 and again from 2013 until present.
In his new role, Snedden will be NZC's representative on the board of the ICC, "a task with which he is very familiar, having been seconded to the role in 2013 and 2014 during Stuart Heal's tenure, as well as being a member of the ICC chief executives committee from 2001-2007", as an NZC statement put it.
"I'd like to thank Greg for the outstanding direction and guidance he's given the board since being elected as chair in 2016," Snedden said in the NZC statement. "It is a measure of the success he has overseen in this role that he has now been elected the ICC chair.
"Equally, I'd like to thank my fellow NZC directors for their support. I know that, together with chief executive David White and his excellent management team, we'll help lead the sport out of this global pandemic and embrace a strong and sustainable future.
"I look forward to working with the members of NZC, the Major Associations and Districts Associations, as well as the New Zealand Cricket Players Association and the wider cricket family in New Zealand."
Snedden has been in senior positions elsewhere too, including as chief executive of the 2011 Rugby World Cup and as a director of the World Masters Games 2017. He is currently part of the NZC Board's Women in Governance project sub-committee, member of the board's High-Performance Advisory Group and director on the board of Women in Sport Aotearoa, and a trustee of the Cricketers' Hardship Trust.
He will, however, have to immediately stand down from his role as consultant lead of One Cricket project, an initiative aimed at reviewing and improving the delivery of cricket in New Zealand.