Richards, the former Sheffield Wednesday chairman, will return to club football when he steps down from his role with the FA Premier League at the end of this month.
The 70-year-old will replace Vichai Srivaddhanaprabha at Leicester and Terry Robinson will join him at the King Power Stadium to work alongside manager Nigel Pearson as director of football after leaving Stoke's academy.
It is understood the Foxes have made the appointments with Financial Fair Play (FFP) in mind.
The forthcoming FFP rules, if broken, carry penalties such as a transfer embargo and last season Leicester's losses were in excess of £29million.
As Vichai Srivaddhanaprabha prepares the club for what he hopes will soon be Premier League football, Richards has been brought in to ensure it is run on a cost-effective basis.
He is a member of the FA's board, chairman of the FA's international committee, president of the European Professional Football Leagues organisation and chairman of UEFA's Professional Football Committee.
Robinson's brief will be to assist Pearson in squad building but he will specifically be asked to concentrate on lowering Leicester's wage bill by jettisoning a number of high earners signed by former manager Sven-Goran Eriksson.