An extensive review of external and internal candidates in recent months failed to produce a more suitable candidate for chairman of the multi-million pound organisation, according to the RNID.
The RNID's voluntary income has tripled during Strachan's five-year tenure as chief executive, and the charity has become more politically influential.
The RNID was voted the most effective campaigning charity by MPs earlier this year and is currently managing a major national NHS hearing aid project.
But the appointment has led to complaints of a "stitch up" among some members of the deaf community and a formal complaint has been made to the Charity Commission.
A Charity Commission spokeswoman confirmed that a complaint was lodged last week, and that the Commission had been in touch with the RNID.
The complaint relates to Strachan's long length of service at the RNID and the fact that he was on the trustee board before becoming chief executive in 1997.
Deaf activists and sign language users expressed their anger online last week, notably through a popular online discussion group run through the web site www.deaf-uk.org.uk.
Some are resentful that the decision was made by the trustees of the organisation on behalf of members and a number of postings urged the deaf community to picket the RNID to ensure the incoming chief executive is deaf.
But the appointment was made according to the organisation's constitution.
Transitions from chief executive to chair of the board of trustees are unusual in the charity sector, confirmed Tesse Akpeki, head of trustee and governance team at NCVO. "It's a tricky situation but not unknown in America, where the two roles can be combined."
Clear definitions of the two roles and good induction processes were needed in this type of situation, said Akpeki. She encouraged outgoing chief executives to take a year-long break before moving on to become chair.
A move from trustee level to chief executive was more controversial than the other way round because it was a move from an unpaid voluntary position to a salaried role, she said.
Stephen Bubb, chief executive of ACEVO, expressed support for the move. "James Strachan is a good role model for the sector and an outstanding chief executive for the organisation."
Former chief executives were less likely to become interfering trustee chairs, said Bubb, because they often had first-hand experience of this themselves.
"Quite a few of our members are chairs of other charities, and many are a little more careful to observe the proprieties because they know how difficult it is if the chair oversteps the line," he said.
The RNID will announce a new chief executive by the year's end.