The money will be used to meet a commitment, made by the government in December, to increase the number of newly-trained educational psychologists from 160 to 206 each year. The extra funding starts in 2020 and will cover three new rounds of training.
In announcing the funding commitment the DfE has revealed the findings of an educational psychologist workforce survey of councils, which are the main employers for the role.
This found that more than two thirds (68 per cent) are finding it difficult to fill vacant posts, leaving insufficient staff to cope with demand.
A similar proportion (66 per cent) said that they had at least one vacancy and 83 per cent said that they consistently experience recruitment problems.
The survey, carried out by the University of Warwick for the DfE, also revealed that only around a half (55 per cent) of councils are actively recruiting to fill vacant posts.
Further research from focus groups found that uncertainty around funding as well as frustration over a consistent failure to recruit are among major factors in this inactivity.
Almost all (93 per cent) councils surveyed said they were experiencing more demand for educational psychologist services than they could meet.
Educational psychologists support children with special educational needs or a disability as well as other vulnerable groups, such as those with mental health problems.
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They also carry out statutory assessments for education, health and care plans (EHCP), which have replaced statements of special needs.
Such statutory work was the most commonly-cited factor in the increase in demand for educational psychologist services.
More than three quarters (78 per cent) of qualified educational psychologists say their workload is increasing and 76 per cent said they never seem to have enough time to get everything done in their job, the survey also found.
In April last year the DfE said it would act to address educational psychologist shortages after recruitment concerns were raised by councils.
Announcing the funds yesterday, children's minister Nadhim Zahawi said: "Every child deserves to be happy, healthy and have the best chance of fulfilling their potential.
"Educational psychologists play an important role in making sure that this is no different for children with additional needs, by providing tailored support and helping families and teachers when there are challenges to overcome.
"We said that we would train more educational psychologists to help meet increasing demand for their services - and today we are confirming funding over £30 million to make this happen.
"We are launching three new training rounds from 2020, which will see over 600 psychologists trained.
"New research published today tells us that too many local authorities have struggled to fill vacancies for educational psychologists.
"This new funding for additional psychologists will mean many more children, their schools and their parents feel well supported to tackle what can often be complex difficulties."