Sir Malcolm Rifkind also stepped down as chair of the House of Commons' Intelligence and Security Committee and said he would not be contesting another election as Member of Parliament.
"I have concluded that to end the uncertainty it would be preferable to step down at the end of this Parliament. This is entirely my personal decision," Rifkind said in a statement.
He, however, continues to deny any wrongdoing and said the allegations against him were "contemptible".
The British Parliament will be dissolved on March 30 in preparation for the General Election scheduled for May 7.
Malcolm, who had been suspended by the Conservative party pending further investigation, first served in the government under Conservative Prime Minister Margaret Thatcher.
A Conservative Party spokesperson said: "Sir Malcolm has had a long career of distinguished service both to the Conservative Party and the country. We respect and support his decision to stand down."
The reporters posed as staff of a bogus Hong Kong based firm and met the MPs to hire them to join the company's advisory board.
In the sting yet to be aired on British television, the two politicians reportedly offered to act on behalf of the fictitious Chinese company at a price of at least 5,000 pounds a day.
Straw, who had earlier announced he would not be seeking re-election as an MP, suspended himself from the party and is being investigated by the Parliamentary Standards Commissioner.
"I have acted in accordance with the parliamentary rules at all times in respect of Senator International, as in all other respects. All of these matters will be scrutinised by the Parliamentary Commissioner," he said in a statement.
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