It has been moved outside of the Republic’s Exclusive Economic Zone (EEZ).
The ‘live-fire’ exercise had been due to take place 240km off the southwest coast.
Irish Foreign Affairs Minister Simon Coveney said the exercises would be “relocated outside of Ireland’s EEZ”.
Mr Coveney had previously said Ireland would not welcome drills being carried out in the EEZ, but claimed the country had no power to stop Russia.
The decision to relocate the exercise had been made as a “gesture of goodwill”, the Russian ambassador to Ireland, Yuri Filatov, said on Saturday.
A group of fishermen who used the area had also warned that they would stage peaceful protests against the action if it went ahead as originally planned.
The Irish South and West Fish Producers Organisation had highlighted the area’s importance for members.
The Irish Junior Minister Michael Noonan had also warned that the planned drills could also have “devastating” consequences for a number of species in the area, including several types of whales.
Mr Filatov previously described the controversy as “overblown”.
The Chairman of the Oireachtas Foreign Affairs and Defence Committee said he was hopeful Mr Filatov would appear to answer the committee’s questions.
While stating that no ambassador was accountable to the Irish parliament, he said there were “significant issues of public interest” that the committee should be briefed on.