The government has always insisted it would not make them compulsory for UK citizens without giving MPs a vote on the issue - and it would not be compulsory to carry them.
It had been planned to make them compulsory for all 200,000 airside workers from 2009 but instead the government announced there would be an 18-month trial, for airside workers at Manchester and London City airports only.
But the pilots union Balpa had complained that its members had effectively been forced into signing up for the cards.
ID cards were initially promoted as an anti-terror measure, but Mr Johnson said they should not have been sold as the "panacea for tackling terrorism" which he said had been responsible for "messing up" the debate.
Mr Johnson added: "People who worked airside were resenting the fact there was compulsion involved.
"Now we can have a much more constructive discussion about the issue if we remove that one element of compulsion.
He added that ID cards were "an important tool for tackling terrorism", but were not "the whole toolbox".
But Mr Grayling rendered the decision made them even more of a "white elephant".
Chris Grayling: "A complete bodge from the government"
"They have spent millions on the scheme so far - the home secretary thinks it has been a waste and wants to scrap it, but the prime minister won't let him," Mr Grayling added.
"This is no way to run the country."
Mr Johnson said it was "nonsense" to suggest he had wanted to scrap the scheme.
Liberal Democrat home affairs spokesman Chris Huhne said the proposed ID cards would now be "nothing more than a second-rate passport".
"This is another nail in the coffin for the government's illiberal ID cards policy, which will soon be so voluntary that only Home Office mandarins seeking promotion will have them," Mr Huhne added.
"These expensive and intrusive plans should be ditched now."
Balpa's General Secretary Jim McAuslan welcomed the decision, which he said was "sensible".
He added that the union would "be stressing to its members the new voluntary nature of the scheme" and "monitoring airport operators to ensure they stick to the new rules and don't bring in compulsion by the back door".
Brian Boyd, national officer of Unite the Union, which represents thousands of airport workers and lobbied against compulsory cards for its members, welcomed what he called a "sensible choice" by the home secretary.
TUC general secretary Brendan Barber said the decision was a "victory for union campaigning".
However, in a statement, the campaign group No2ID said the "humiliating climbdown" was not the end of the scheme.
"It's just part of the ongoing attempt by senior Home Office officials to fortify the scheme against cancellation and to bind the hands of a future government," the statement added.
The rollout of the ID card scheme will be accelerated on a voluntary basis for UK citizens, starting in Greater Manchester by the end of the year.
Residents in other locations in the North West of England will be able to apply from early 2010, while the government's intention is to roll out the scheme in London in the same year - 12 months early.
Some 3,500 UK citizens have already applied for the cards.
But the Tories - who say they will scrap the scheme if they win the next general election - have written to five firms bidding to supply ID cards warning them not to sign any long-term contracts.
Shadow Immigration Minister Damian Green accused Mr Johnson of a "flagrant breach" of a ruling by the Speaker that ministerial announcements must be made first to the Commons by briefing the media before he released a written statement.
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