The Oxford director will replace Greg Clarke after the annual general meeting on 10 June, when league clubs will be asked to ratify the appointment.
Clarke said last year that he would leave the role he has held since 2010.
Lenagan, who is the chairman of rugby league side Wigan, has been on the Football League's board since 2013.
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Ian Lenagan is set to become the Football League's new chairman after he was unanimously recommended by the organisation's nomination committee.