Failing to secure a qualification in Maths or English is one of the key reasons apprentices do not complete courses.
But EDSK, an education think tank, previously found a majority of those who dropped out of apprenticeships also cited "poor quality" schemes, highlighting a lack of training and bad management.
Other bodies would like to see the government go further.
David Smith, chief executive of Lifetime, England's largest apprenticeship provider, welcomed the rule change, saying it would help address a significant barrier for many apprentices, particularly those who are considered most disadvantaged.
But Mr Smith said he was "disappointed" the change was not extended to apprentices aged 16-18.
The Learning and Work Institute, however, believe it is a mistake to reduce the minimum length of an apprenticeship, and criticised the government decision to remove any requirement for those over 19 to obtain qualifications in English and Maths.
"England is already an outlier compared to other countries, with shorter apprenticeships and far less general education like English and Maths.
"Lowering standards in this way will increase this disparity," said chief executive Stephen Evans.