The EA will also try to cut the money it spends on school transport.
The authority described the increasing cost of taxis as "of significant concern".
The EA said that the total annual bill for taxi use had more than doubled in five years - growing from just under £20m in 2020/2021 to almost £40m in 2024/2025.
The EA also said it would end some agency contracts and reduce overtime payments across its own workforce.
"Education services in NI have faced growing and increasingly unsustainable budgetary shortfalls for a number of years," the EA said in a statement.
"Living within allocated funding - whilst meeting rising service needs - has been an increasing challenge."
"The Education Authority has therefore regrettably been required to identify a series of significant savings measures."
The authority hopes to make up to £30m in savings from the measures it has announced, but said that the EA board had not supported other undisclosed savings measures due to the scale of their potential impact.
Further savings may require law or policy changes from MLAs.
Separately, Stormont's Public Accounts Committee (PAC) recently reported that many schools in Northern Ireland "are in a state of disrepair," and it would take up to £800m to fix them.