The former state monopoly ISP, which is now privately owned, has agreed to give two warnings to subscribers before cutting them off.
Record industry group the International Federation of the Phonographic Industries (IFPI) said that it would be taking action against other ISPs to ensure they did the same.
"The record companies will supply Eircom with the IP addresses of all persons who they detect illegally uploading or downloading copyrighted works on a P2P [peer to peer] basis," said a statement from the IFPI.
"Eircom has agreed that it will from now on implement a graduated process," it said. "The record companies have agreed that they will take all necessary steps to put similar agreements in place with all other ISPs in Ireland."
The case involved the four major labels EMI, Universal, Warner and Sony.
Eircom said that when it received the labels' list of people they suspected of engaging in illegal file-sharing, it would tell its customers that infringement had been detected.
If the activity continues Eircom will warn the subscriber that they will be cut off if there is no change in behaviour. If the file sharing continues the customer will be disconnected.
EMI Ireland managing director Willie Kavanagh is also the head of the Irish Recorded Music Association (IRMA), which is affiliated to the IFPI.
"[This is] something we've had to work together to make sure this got to a stage where we can deal with what is an enormous difficulty within the Irish and worldwide record business," he told broadcaster RTE.
The 'three strikes and you're out' policy is a popular one with rights holders, who are lobbying Governments across Europe to force ISPs to implement it.
The UK Government stopped short of including such a demand in its Digital Britain report last month. It said that it plans to force ISPs to pass details of subscriber activity to rights holders but did not demand that they disconnect users.