The former work and pensions secretary said he remained a committed supporter of the new Prime Minister, who he backed in the leadership contest, but has chosen to remain on the backbenches.
It followed reports that he had been lined up for the position of leader of the House of Commons in the new administration.
“I have been offered (a job) and said I won’t be taking it up. I’m going back to the backbenches again,” Sir Iain told BBC Radio 4’s The World At One.
“I am very happy to support her. Sometimes in life you have got to figure out whether you add value to a particular job that you are being asked to do.
“It is all about what I can do and I am very happy to be on the backbenches for the moment.”
Earlier, Nadine Dorries confirmed that she had been asked by Ms Truss to stay on as Culture Secretary but had decided that she also would be returning to the backbenches.
Her voluntary departure is expected to mark the start of a significant clearout of ministers as Ms Truss shapes her top team.
Priti Patel has already quit as home secretary, having seen her position publicly linked with Suella Braverman, the Attorney General.
Deputy Prime Minister Dominic Raab – who backed Rishi Sunak in the leadership contest – is also expected to be among the casualties having denounced Ms Truss’s tax plans as an “electoral suicide note”.
Mr Sunak, the former chancellor whose resignation helped trigger the downfall of Boris Johnson, has also made clear he does not expect to be offered a new job.
His supporters, however, have been urging Ms Truss to appoint an “inclusive” Cabinet and not simply surround herself with loyalists in the way that Mr Johnson was accused of doing.
Ahead of the formal announcements, a number of the most senior positions have already become clear with Business Secretary Kwasi Kwarteng set to take over as Chancellor and Education Secretary James Cleverly becoming Foreign Secretary.
Work and Pensions Secretary Therese Coffey – regarded as Ms Truss’s closest confidante at Westminster – is expected to be the new Health Secretary and Deputy Prime Minister, while Mrs Braverman is heading for the Home Office.
Ben Wallace is set to remain as Defence Secretary, but there is less certainly over other appointments.
There were reports that Ms Dorries is being replaced at the Department for Digital, Culture, Media and Sport by Michelle Donelan, the formed universities minister who served briefly as education secretary only to quit almost immediately in the wave of resignations which brought down Mr Johnson.
Jacob Rees-Mogg, the current Leader of the Commons, is reportedly set to be the new Business Secretary, while Mr Johnson’s long-time ally Kit Malthouse is being linked with Education.
There were suggestions that two of Ms Truss’s defeated leadership rivals – Kemi Badenoch and Penny Mordaunt – have been offered International Trade Secretary and Leader of the Commons, respectively
Ms Truss is however reported to be struggling to fill the post of Northern Ireland Secretary.