Wrenn, who has held the post for the last two years, wrote to RIAS council members explaining she could not 'commit to the length of time needed to steer the next phase of the [RIAS'] development'.
Credited for the reintroduction of the incorporation's competition unit, Wrenn admitted she was pleased to have been a catalyst in the 'first stages of the transformation' of the RIAS.
She said: 'I would like to take the opportunity to thank all those members and staff colleagues who have worked with me in facing the sometimes testing challenge of bringing about necessary change at the RIAS - and to say how much I have enjoyed getting to know better Scotland's rich built heritage and creative contemporary architectural culture.'
She added: 'The practice environment presents many challenges, ranging from the retention of Scottish talent and building an internationally recognised design profile, to the battles over procurement methods and the need to create truly sustainable communities.'
The RIAS said the recruitment process for finding Wrenn's successor would be as normal for any other position.