Third-level institutions will not be holding written, oral or practical assessments in examination centres during the Covid-19 emergency.
Universities and colleges have finalised alternative assessment arrangements - with options including online exams, written assignments or rescheduling.
These have been communicated to all students.
It comes as a decision on whether State exams will go ahead as planned is yet to be announced.
Mr Varadkar said Minister for Education Joe McHugh and the State Examinations Commission are drawing up options to allow the State exams to be held.
He said there are a "number of options" and Minister McHugh is working to ensure that "by hook or by crook" the exams take place.
He said the Government did not want people who are hoping to enter third level education later this year "to lose a year ... or half a year" of their lives.
Mr Varadkar also said they were keen to avoid the "problems that would follow" from there not being an entry year into colleges in 2020.
There are 126,000 students due to sit the State exams in 2020.