Lord Hodgson’s departure comes after four and a half years in the non-executive position.
Meanwhile, Mike O’Brien, the managing director of TenetConnect and TenetSelect, has been appointed to the board as group brands director.
The changes follow former CEO Simon Hudson’s departure in July, after which Greenwood was appointed to the role on an interim basis.
Greenwood said: “Tenet has made notable progress during Lord Hodgson’s chairmanship and he leaves the group at a time when it is recognised as being one of the financially-strongest in its chosen sector.
“Moreover Robin has been instrumental in helping to position and prepare the business to fully support both independent and restricted advisers in the post-RDR environment.
Two further independent non-executive directors will be appointed to the Tenet board “in due course”.
