In a statement, the hospital said that its board accepted proposals from Chairman Lyndon MacCann at a full board meeting last night.
The development follows the controversy over unread X-rays and unopened GP referral letters.
The main reforms will see the introduction of a board of management of ten and a review of the size and structure of the 22-member hospital board by consultants PricewaterhouseCoopers.
The board of management will include external members 'representing patient interests, business and financial skills'.
The hospital says that any alterations to the full hospital board may require legislative changes to its statutes.
A new post of Director of Quality will also be established.
PwC was commissioned in 2009 to examine existing governance arrangements and senior management structures at the hospital and presented its report last autumn.
Health Minister Mary Harney said she welcomes any steps that can be taken to improve the governance of Tallaght Hospital so that roles are clarified and procedures are streamlined.
She said that the only priority must be that the new arrangements will benefit patients.
