The conservative firebrand whom the Trump administration installed as a No. 2 at the FBI announced Monday that he is resigning from the bureau.

Andrew Bailey, the former Missouri attorney general who has supported debunked claims that the 2020 election was stolen, told bureau employees in an email that he was leaving to spend more time with this family, according to three people familiar with the personnel move who spoke on the condition of anonymity to discuss a matter they were not authorized to speak about.

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Bailey, who was hired for the leadership role a...