The artillery drills were to take place at the start of February in international waters, but within Irish-controlled airspace and the country’s exclusive economic zone.
The planned drills had caused considerable upset and controversy in Ireland.
Mr Coveney tweeted: “This week I wrote to my counterpart, the Minister of Defence of Russia, to request a reconsideration of naval exercises off the Irish coast.
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“This evening I received a letter confirming the Russian exercises will be relocated outside of Ireland’s EEZ.
“I welcome this response.”
In a statement, the Russian ambassador to Ireland Yury Filatov said: “In response to the requests from the Irish government as well as from the Irish South and West Fish Producers Organisation, the Minister of Defence of the Russian Federation Sergey Shoigu has made a decision.
“As a gesture of goodwill, to relocate the exercises by the Russian Navy, planned for February 3 to 8, outside the Irish exclusive economic zone (EEZ), with the aim not to hinder fishing activities by the Irish vessels in the traditional fishing areas.”
Irish fishermen had planned to travel to the area to disrupt the Russian naval plans in a bid to protect their fishing stock.
Representatives of the Irish fishing industry met the Russian ambassador to Ireland on Thursday, later claiming to have been a given a guarantee that their fishing grounds will not be affected by the navy exercises.
That claim was partially disputed by a spokesperson for the Russian embassy, who said it was “not true” that an agreement had been reached on “buffer zones” in the area for fishing boats.
The Department of Transport had also issued a marine notice that the Russian navy was set to carry out manoeuvres off the south-west coast of Ireland from next Thursday.
It is not known where the naval exercises will now take place.