However, the Irish Aviation Authority has warned that it may take up to three days for full services to resume.
The Authority emphasised that the lifting of restrictions is subject to the ash cloud not moving over Ireland and no further aggressive activity from the Eyjafjallajokull volcano.
It said: 'The IAA continuously monitors the situation and will issue a statement if the exclusion zone threatens Irish airspace today or in the days to come.'
There will be limited flight operations from Dublin and Cork airports during the day and Shannon Airport has confirmed it is to remain open.
Speaking on RTÉ's Morning Ireland, Siobhan Moore of the Dublin Airport Authority said it will begin 'a phased and slow return to business' today.
Two transatlantic flights arrived at Dublin Airport this morning from Atlanta and Philadelphia.
Check-in desks are open at Shannon Airport to process travellers on the Aer Lingus service to New York, which is due to depart this afternoon.
The first inbound flight for several days arrived at Belfast International Airport late yesterday evening and services are expected to get back to normal there throughout the day.
It is expected that today's flights will focus on positioning aircraft and crews and full service by the airlines may take up to three days to resume.
Passengers are advised to check with their airline's website before travelling to airports.
Aer Lingus expects all services to resume from 1pm this afternoon.
Ryanair's flights between Ireland and the UK have been halted until Friday afternoon, but it hopes to resume other European services tomorrow.
Much of European airspace has reopened and Europe-bound planes have left Asian airports on schedule.
European air traffic agency Eurocontrol says about 75% of flights will operate in Europe today.
The International Air Transport Association has said the crisis cost the industry €150m a day.
IATA chief Giovanni Bisignani told Italian television that more than five medium- and small-sized European airlines risked bankruptcy in the fall-out from the ash cloud shutdowns and called for EU compensation.
In Iceland, police said the plume of ash from the volcano, which began erupting last Wednesday, was diminishing but warned that there was 'still considerable volcanic activity at the site'.
The World Meteorological Organisation said the ash was expected to head towards the Arctic when the weather changed later in the week.
Meanwhile, the Department of Defence says that Irish troops due to return from Kosovo are expected to be able to board a plane in Pristina later today.
The aircraft is currently in Prague and will arrive in Pristina in the next couple of hours to pick-up the 160 Irish troops due to redeploy back home following their six-month tour of duty in Kosovo.
The plane is now due to arrive in Dublin Airport at 3.15pm this afternoon.