Forty-seven-year-old Gandhi responded to the leaders on Twitter, saying, "thank you".
The leaders hoped that Gandhi would strive for the welfare of the people, put up a fight to protect secular fabric of the country.
Former Bihar deputy chief minister and RJD leader Tejashwi Yadav lauded Gandhi for "redefining" Indian politics.
Yadav said Gandhi has proved his mettle in inclusive, secular and liberal politics. The RJD leader said the youth feels "duped and cheated" under the current BJP-led NDA regime.
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Referring to a line "that there are many promises to keep, miles to go before I sleep" from Robert Frost's poem, CPI(M) general secretary Sitaram Yechury hoped it would be the guiding motto for Gandhi during his stewardship of the Congress.
"In Indian politics, we wish all those who have taken up new responsibilities the best. Our wishes to him in discharging these responsibilities only with the hope that it will be in the interest of the people and the country," he said in a video message on the Congress's Twitter handle.
In a video message posted on the Congress's Twitter handle, Samajwadi Party chief Akhilesh Yadav noted Gandhi's responsibilities have now become greater and hoped he would make consistent efforts to take the grand old party forward.
DMK working president M K Stalin also joined the leaders in wishing Gandhi, hoping he would restore glory of secularism.
"Am confident that he will fulfil the aspirations and hopes of the people and restore the glory of Secularism, Socialism and Federalism. @OfficeOfRG," Stalin tweeted.
"New Energy, Newer steps, New Challenges & Navsarjan! Under the leadership of Rahulji, We shall write a golden chapter for Our Nation!" Surjewala tweeted.
Gandhi succeeds his mother Sonia Gandhi, who led the party for the last 19 years.
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