The vote was called after Deputy Speaker Charoen Chankomol said he had invited the five MPs who submitted the six bills for talks and they had all agreed to withdraw their draft legislation.
The bills were widely seen as aimed at allowing ex-premier Thaksin Shinawatra, convicted of corruption, to return to the country without facing jail time.
Their promulgation sparked widespread protests around the country, with thousands arrivijg every day in the capital to join proposed massive marches to disrupt Bangkok and force the government of Mr Thaksin's sister, Yingluck, to back off.
Of the six items of legislation, five are "reconciliation bills" proposed by Gen Sonthi Boonyaratkalin, Niyom Worapanya, Samart Kaewmeechai, Peerapan Palusuk and Nattawut Saikuar.
The other is an "amnesty bill" proposed by Niyom Worapanya. Mr Niyom proposed two bills - one named as a reconciliation bill and the other an amnesty bill.
All five MPs rose to confirm they wanted to withdraw their legislation and asked for House approval.
The House voted 310-1 to approve the request.
Mr Charoen adjourned the House meeting immediately after the vote.
Gen Sonthi, who proposed one of the reconciliation bills, told the House that he agreed to withdraw his draft in response to the calls by people in various sectors.
"Before, I did something that many people branded as undemocratic," the former coup leader said.
"Today I am in parliament, I want everything to be done through parliamentary channels.
"I therefore ask for your permission to withdraw the bill."
Gen Sonthi led the Sept 19, 2006, military coup that ended the Thaksin Shinawatra administration.
Although these six bills have been withdrawn, one more amnesty bill, proposed by Pheu Thai MP Worachai Hema is due to be discussed by the Senate on Monday.
That bill is already seen as flawed, and could be held up indefinitely in the Senate, or referred to the Constitution Court on the grounds that it contravenes the constitution.
Alternatively, it might be amended by the Senate to cover only people involved in the Rajprasong events of 2010 who did not commit "serious" crimes, before being sent back to the lower house.
The Senate has the power to "vet" the bill, a process that has no deadline, and which might be used to kill the bill.
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