Rahane returns to lead Royals for the game against Delhi Capitals on Saturday after Smith replaced him as captain in the middle of the season following the team's disappointing run which saw it lose six out of their first eight games.
However, there was a revival of fortunes of the side under Smith which led Royals to winning three out of the last four games, giving them a slender hope of making the play-offs with a game to go.
Smith has returned home to join the Australian team ahead of the World Cup beginning May 30 in the UK.
"We have requested Ajinkya to take on the captaincy of the team; as a true Royal he has shown great courage and character in graciously accepting the responsibility, which accompanies this role, whilst it would have been easier for him to take a back seat and focus solely on his batting," said Zubin Bharucha, Head of Cricket at Rajasthan Royals.
"A true team man and a true Royal, we are extremely fortunate to have characters like him playing this sport and even prouder he is part of the Rajasthan Royals franchise.