Mr Leigh is a former Conservative Party treasurer and is the president of Westminster Synagogue.
Finchley United Synagogue chairman Jon Mendelsohn will become a Labour peer.
Mr Mendelsohn, a former Union of Jewish Students chair, is a business adviser and co-founder of LLM Communications.
The trio are among 30 new peers set to join the Lords following nominations from the political party leaders. Their suggestions are vetted by the House of Lords appointments commission.