Richardson is in place as temporary director general of customer compliance following the resignation of Jennie Granger in April. Granger led the compliance department for five years.
McLean will take over as head of customer services from Ruth Owen, who left after only one year in the job.
Richardson was previously director of counter-avoidance at the Revenue. Before that he was director of central policy and director of specialist personal tax.
McLean was already part of the customer services team as its director of finance and planning. Previously she was a director at Transport for London.
Owen and Granger announced their resignations in quick succession earlier this year. Owen said it was a “difficult” decision to leave, but added she has been offered a “one-off opportunity to try a different career in the private sector". Granger also said that she is moving into the private sector.