Ms Sturgeon said she wanted a vote to be held between the autumn of 2018 and the spring of the following year.
European Union negotiator Michel Barnier previously insisted that the bill had to be settled when Article 50 is triggered, but, according to the BBC, he has since sent a message to Brexit secretary David Davis through "informal channels" dropping the demand.
In 2014, voters in Scotland rejected a similar independence referendum by a margin of 55 percent to 45 percent.
The bill will then return to the Lords on Monday night, where it is expected to pass swiftly in deference to the will of the Commons.
Concerns over a second referendum vote will tend to unsettle Sterling to some extent even though there is no possibility of a vote within the next 18 months and the United Kingdom government remains strongly opposed to a another vote.
Prime Minister Theresa May has said for months that she would invoke Article 50 of the EU's key treaty, the trigger for two years of exit negotiations, by March 31.
Sturgeon hopes her country could retain access to the European single market if it breaks away from the rest of the UK.
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Issues such as the sudden return of a customs border between Northern Ireland and the Republic of Ireland, a gap in regulations and confusion about the future of United Kingdom citizens in the European Union and vice versa were among the consequences of a "no deal" situation highlighted by the committee.
Some rebels admit in private that they are unlikely to muster sufficient numbers to prevent a government victory on Monday evening, not least because the Democratic Unionist party and some Labour MPs are likely to support Mrs May.
Labour Leader Jeremy Corbyn responds to the prime minister's speech.
"Now more than ever we need an inclusive government that listens and acts accordingly".
"The Liberal Democrats will keep fighting to give the British people the final say on the deal, so that a hard Brexit isn't imposed on the country that nobody voted for".
How soon the European Union can proceed will largely depend on when May triggers Article 50, and if leaders can hold their summit on the preferred date of April 6.
"These people are not bargaining chips".
The EU's chief negotiator Michel Barnier is reported to take a position that the Brexit divorce deal would have to be finalised before any future arrangements are negotiated. Facing a possible rebellion from Conservatives who want to vote on the final Brexit terms, Davis urged lawmakers to back May's Brexit strategy and overturn those changes because they would tie the government's hands in the negotiations.