"I am too excited to gain a place in your hearts, once again. I hope to bring happiness in your lives like you all did in every moment of my life, " Rekha said during her first public appearance after becoming MP at a function in Mumbai on Friday night.
"I will work from the bottom of my heart, " Rekha said.
"I will continue to entertain you and make you absolutely proud of me, " she said.
President Pratibha Patil has approved the names of Rekha and cricket icon Sachin Tendulkar for nominated seats the Upper House of the Indian Parliament.
Entrepreneur and social worker Anu Aga's name has also been approved for a nominated seat.
This follows a letter that Prime Minister Manmohan Singh had written to President Patil with the Congress-led United Progressive Alliance (UPA) government's recommendations for the seats.
The Congress party proposed to nominate Rekha and Sachin in the President's quota.
With Rekha and Sachin accepting their nominations, they became Members of Parliament (MPs) under a provision of the Indian Constitution that allows the President to nominate 12 members to the RS.
Under article 80 of the Constitution, the Rajya Sabha is composed of not more than 250 members, of whom 12 are nominated by the President of India from amongst persons who have special knowledge or practical experience in respect of such matters as literature, science, art and social service.
The names are approved by the President usually after being notified of the recommendations by the Prime Minister through the Ministry of Home Affairs that finalises the names after receiving consent from the proposed nominees.