The resignation of 52-year-old Sidhu, who was nominated on April 22, has been accepted by Chairman Hamid Ansari with immediate effect, the House was informed today.
While he made a brief statement indicating all was not well with him in the BJP, there is talk of Sidhu joining the AAP ahead of the elections.
"People can give their rt hand for an RS seat. Ever seen a sitting RS MP resigning to save his state? I salute Sidhu ji for his courage," Kejriwal, who is currently touring Punjab, tweeted.
Top AAP sources said Sidhu will join the party in a few days' time. There was speculation that Sidhu may be in the race for AAP's chief ministerial candidate in the state.
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Top AAP leaders Sanjay Singh and Lok Sabha member Bhagwant Singh Mann welcomed Sidhu's decision to resign from Rajya Sabha but parried questions whether he would join the party and become its chief ministerial face.
"At the behest of the honourable PM, I had accepted the Rajya Sabha nomination for the welfare of Punjab.
"With the closure of every window leading to Punjab the purpose stands defeated. It is now a mere burden. I prefer not to carry it.
"In the war of right or wrong, you can't afford to be neutral rather than being self-centered. Punjab's interest is paramount," said the former cricketer-turned politician, who had represented Amritsar in the Lok Sabha between 2004 and 2014.
His wife, Navjot Kaur, who is Chief Parliamentary Secretary in Punjab where BJP shares power with Akali Dal, had created a flutter on April 1 (April Fool's day) announcing her resignation from the BJP.
"The burden is over," she had written on her Facebook post on April 1, but after a meeting with top BJP leaders in Delhi, she said, "All is well" and she is very much a part of BJP in Punjab.