The Bill, which gives the government the power to begin Brexit talks, is being debated in the Lords, with next week set aside for discussions of amendments.
Writing in the Mail on Sunday, Heseltine said tweaks to give parliament more power over the process were reflected in last month's Supreme Court ruling, which forced May's ministers to draft the Bill.
Labour and Lib Dem peers have long been confident of their chances of amending the Bill, but Heseltine is the first big name Conservative peer to back their efforts, lending his support to clauses which would hand parliament a "meaningful" vote on the terms of Brexit, and potentially force May back to the negotiating table.
"In the end, the outcome of Brexit will have to be confirmed by parliament. It will also have to pass in 27 European parliaments, several sub-national parliaments and the European parliament,” Heseltine said.
“It was perhaps unwise for our government to suppose that our parliament should be excluded where all others were included. Very sensibly, after the Supreme Court interpreted the law, that position was reversed and parliament was restored to its rightful constitutional role as the ultimate authority.
“I will vote in the House of Lords to ensure that position is legally intact. This is not a confrontation with the government which has already made such a commitment. It is – put simply – a decision to ensure that the Commons has the chance to define its role in the exercise of its authority over what most people regard as the defining issue of our time.”
The former Tory minister also said parliament must be able to halt the Brexit process if public opinion shifts away from quitting the EU.
“My opponents will argue that the people have spoken, the mandate [is] secured and the future cast,” he said.
“My experience stands against this argument. At the moment there is no evidence that public opinion has changed. The PM rides high in the polls. But what if this changes?”
Responding to Heseltine's comments, home secretary Amber Rudd played down the rift between him and and the government.
However, in an appearance on ITV's Peston On Sunday, she conceded: “I hope he'll reconsider. There will be plenty of opportunities to debate [the Bill]. I'd like it unamended.”
The House of Lords will debate amendments between 27 February and 1 March, with a final vote scheduled for 7 March.
After peers approve the Bill it will enter a final phase of "ping pong" where the Commons and Lords will seek mutual agreement on the text of the legislation before it can be granted royal assent by the Queen.
The government hopes to pass the Bill in time for May to trigger Brexit talks by the end of March.