Parents and grandparents who work in Amazon warehouses will be able to choose to work in term-time only.
Amazon said the new contract will mean people with children to look after can take six weeks of holiday in summer and two weeks at Easter and at Christmas.
But the GMB union, which is fighting Amazon for recognition, said that while flexible working is welcome, most workers want better wages.
"What they're telling us is they can't live on poverty pay," said the GMB.
Amazon's regional operations director, Neil Travis, said he hopes the flexible working will encourage more people back into the workplace.
"We spent a lot of time listening to our employees and one of the things that we were learning is that they really wanted more flexible opportunities," Mr Travis said.
He added that the contract still entitles people to full-time benefits.
Claire McCartney at the Chartered Institute of Personnel and Development said that only 4% of workers have term-time working.
''With the cost and availability of childcare causing huge challenges for working parents, term-time working is likely to have a positive impact on attraction and retention at a time when organisations are struggling with skills shortages," said Ms McCartney.
Amazon is offering the new contract just as it is trying to fight a bid by the GMB to be the first trade union in Europe to be recognised by the company.
The company employs more than 70,000 people in the UK. Amazon said that it does not believe that union recognition is appropriate.
It said that it prefers to talk directly with its employees rather than go through a union.
Workers at Amazon in Coventry have been on strike for 16 days this year. They are calling for an increase in their hourly wage to £15 an hour.
The GMB's senior organiser, Amanda Gearing, said that more flexible staff contracts are positive but the priority for the workforce is improved pay.
"I don't think this is what they're looking for right now," she said. "They want more money in their pocket, what they're telling us is they can't live on poverty pay."
Amazon said the rates of pay are competitive and that it recently increased wages by 10%.
The GMB said that a majority of workers in the Amazon Coventry warehouse want union representation and it has applied to the Central Arbitration Committee (CAC) for statutory recognition.
The union said that 800 Coventry employees are now members and that this represents a majority of the workforce.
Mr Travis would not be drawn on whether the company would be prepared to recognise the GMB if they could prove majority support among the Coventry workforce.
"The GMB have made a formal application to CAC and we are working with the CAC as part of that process. We continue to focus on engaging directly with our employees and we continue to offer a really attractive rate of pay and comprehensive benefits," Mr Travis said.
But in its submission to the CAC, Amazon could argue that there are more people working in the warehouse than GMB calculates, and this could lead the CAC to deny the GMB recognition.
The committee could take several weeks to reach a decision.
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Amazon to offer parents term-time-only working
