European Central Bank President Mario Draghi has told a monthly news conference that the move to cut interest rates was a "unanimous decision."
The ECB's policy-setting governing council voted to lower the rate for its main refinancing operations by a quarter of a percentage point to 1.25%.
In a statement this evening, Permanent TSB confirmed that it would pass on the rate cut to both its variable and tracker mortgage customers. The cut in rates will be effective from 21 November.
The new SVR rate for Permanent TSB bank, after this cut is introduced, will be 5.44%.
Bank of Ireland has yet to take a decision on whether to pass on cut to its variable mortgage customers.
A spokeswoman said that all its rates were subject to "regular review". She said that the cut would be passed on to tracker mortgages and this usually happened within five days.
Ulster Bank said it had no plans to pass on the ECB rate cut to its variable rate mortgage customers.
The bank will pass on the 0.25% reduction to its tracker mortgage customers and says the change will come into effect between 16 November and 1 December.
A spokeswoman said all its mortgage products were under continual review.
EBS said it would pass on the interest rate cut to its tracker mortgages, but that it had not yet made a decision on whether to pass it on to variable rate mortgages.
An AIB statement said: "Our products and services including mortgage rates are under constant review.
"Unlike all of its main competitors, AIB has not increased its standard variable rates since August 2010.
"AIB did not pass on the two 0.25% rate increases (in April and July 2011). Our standard variable rate for owner occupiers is currently 3.25%. Loan to value standard variable mortgages for owner occupiers range from 3.09% to 3.49%."
European stock markets, severely depressed by the Greek-eurozone debt crisis, rallied strongly on the news.
But the move came as a surprise as ECB watchers had not expected new ECB chief Mario Draghi to announce any cut in interest rates so soon after taking over from Jean-Claude Trichet of France.
The Italian former Goldman Sachs banker explained the reasoning behind the decision at his first-ever news conference as ECB chief this afternoon.
Mr Draghi said he saw "high uncertainty" and "intensified downside risks" for the eurozone economy in coming months.
"What we are observing now is ... slow growth heading towards a mild recession by year-end," Mr Draghi warned.
"A significant downward revision to forecasts and projections for average real GDP growth in 2012 (are) very likely."
