According to the page Examiner recruitment and training at IELTS.org, applicants for the job of IELTS examiner must have
a) An undergraduate degree or Master’s degree or qualification(s) that can be demonstrated to be equivalent to an undergraduate degree or Master’s degree (3 years’ full-time academic study, or a minimum of one year’s full-time academic study in the case of a Master’s degree).
b) A TEFL/TESOL qualification from a recognised institution (certificate level or above)
A degree in education (if supported by an undergraduate degree which includes studies focused on English Language)
c) Substantial relevant teaching experience, the majority of which must relate to adult students (16 years and over).
So you don't need to be a native speaker, but meeting the above requirements will not automatically make you an IELTS examiner:
Applicants must then be approved by a qualified examiner trainer. After approval, the applicant undertakes face-to-face training conducted by an accredited IELTS examiner trainer and a certification assessment.
The process to become an IELTS examiner consists of six steps:
All applicants for the post of examiner must have the qualifications and experience outlined above. Shortlisted applicants are invited to interview. The applicant’s professional attributes and interpersonal skills are assessed at three stages in the recruitment process: application form, interview and training.
It is not clear what the training in this first stage involves, since training is what the third stage is about.
Following an interview, successful applicants complete an induction process.
IELTS examiners obviously need to know what IELTS is, how tests are organised, how scoring works, etc. (Applicants have not necessarily taken an IELTS test in the past, especially if they are native speakers.)
Applicants who successfully complete induction proceed to training in Writing and Speaking assessment, which is carried out by an examiner trainer and lasts four days.
Although no further details are given, one can assume that IELTS wants to ensure high validity and reliability for its tests. Validity refers to the ability to test what you claim to test. Reliability refers to the ability to consistently yield the same results when a test is repeated. One of the goals is to achieve high inter-rater reliability, i.e. when two examiners evaluate the same test, the result is the same (or at least very similar). See also the page Valid and Trusted Language Tests on the website of ALTA Language Services.
Applicants then complete a certification set to demonstrate that they can apply the assessment criteria accurately and reliably. If successful, they become qualified examiners.
This test verifies that the applicants can evaluate IELTS exams accurately and reliably; see the discussion of validity and reliability, above.
The two final stages are not strictly part of the recruitment process but about what happens after you've been certified. They ensure accuracy and reliability of IELTS evaluations in the long term:
Examiners are monitored by examiner trainers up to four times a year and at least once every two years. New examiners (and those who have not recently worked as IELTS examiners) are monitored at least three times in their first year. All examiners receive written feedback on their ratings and also on the delivery of the Speaking test. They may be required to take corrective action if any issues are raised about their performance.
6. Standardisation and re-certification
Standardisation is completed at the centre and takes place as close as possible to the 2-yearly re-certification of the examiner. After the standardisation session, the examiners then complete a new certification set to demonstrate they can apply the assessment criteria accurately.
IELTS examiners are not recruited by IELTS directly; that is the responsibility of the test centres.
See for example the page Become our IELTS examiner at the British Council Thailand. This page contains much the same information as the IELTS page cited above but also offers a few downloads, such as a "Guide to applicants for IELTS Examiner recruitment" and an "Examiner Application Form".