This will make it easier for people with conditions such as anxiety disorders or brain injuries to travel to work, socialise and access shops and services.
It is the biggest change to the blue badge scheme since it was introduced in 1970.
Around 2.4 million people with physical disabilities in England already have a badge.
Depending on the location, the permits often enable holders to park free of charge in pay and display bays and for up to three hours on yellow lines, while in London they exempt holders from the congestion charge.
Transport Secretary Grant Shapps said: "We know that for some people, the possibility of not being able to find a parking space can make even leaving the house a challenge, which is why the blue badge is so important.
"The scheme, which is already a lifeline for so many disabled people, will make a huge difference to those with non-visible conditions such as autism, dementia, Parkinson's and arthritis.
"It is my sincere wish that these changes will improve even more people's lives."
Councils assess applications for blue badges and not everyone with a hidden disability will qualify for one.
National Autistic Society head of policy Tim Nicholls said: "We are delighted to see the new blue badge rules come into force.
"This will be a huge relief for thousands of autistic people and their families in England, many of whom are so anxious about things going wrong that they find it hard to leave the house at all.
"A blue badge can be life changing. To live up to this promise, it's absolutely essential that council officials making decisions about blue badges understand autism and the challenges autistic people can face getting out and about."
Local authorities are being given £1.7 million of Government funding in the first year of the extended programme to help cope with the expected spike in demand.
The expanded scheme coincides with the launch of a review to help local authorities tackle fraudulent use of the badges.
Analysis of DfT data by the PA news agency found that 94 out of 152 English councils did not pursue anyone for abusing the scheme in 2017/18.
How to apply for a blue badge
You’ll need a recent digital photo showing your head and shoulders.
You’ll also need a photo or scan of your:
- proof of identity (such as a passport or driving licence)
- proof of address (less than 12 months old)
- proof of benefits (if you get any)
You’ll also need to know:
your National Insurance number (if you have one)
the details of your current Blue Badge (if you’re reapplying)