Under the agreement, the Government guaranteed that there would be no compulsory redundancies or further pay cuts for public servants in return for cooperation on a reform agenda.
Up to now the TUI had rejected the agreement.
hoevver, the union decided to re-ballot members in two separate ballots for 2nd level teachers and 3rd level lecturers - and members have now voted to accept it.
The turnout was 56%.
75% of second level teachers accepted the agreement, which will require them to do an extra hour a week.
However, the margin was tighter for third level lecturers - with only 55% backing the deal.
TUI General secretary Peter McMenamin pointed out that third-level teachers face more significant demands under the agreement.
The Irish Federation of University Teachers is now the only union remaining outside the Croke Park deal.
Earlier today, Minister for Public Expenditure and Reform Brendan Howlin said that public servants who did not sign up to the agreement would not benefit from its protection from compulsory redudnancies and pay cuts.
