"He played an important role during the sale and the board thank him for his support," said a Leeds statement.
"Board director and Geoffrey's son David will take over responsibilities and duties with regards to all contract and transfer enquiries involving Leeds players," the statement added.
"Geoffrey, for personal and health reasons, has reluctantly decided to concentrate his time and energy on his personal life.
"The board of Leeds United has accepted his decision and wish him all the very best for the future."
Many Leeds fans expressed their concerns about Richmond, mainly because of his record as chairman of Bradford City when they won promotion to the Premiership.
He earned a £2.3m dividend from the club after they avoided relegation in their first season but left Bradford 18 months later, shortly before they went into administration.