Sources in the Rajya Sabha secretariat said the Chairman, M Venkaiah Naidu, will administer the oath to Shah on Friday.
The BJP chief is making his debut in Parliament. He was elected to the upper house from Gujarat earlier this month.
The BJP lacks majority in the house. Shah's entry into the Rajya Sabha is likely to give a a boost to the party.
Shah has been a five-term MLA in the Gujarat assembly.