Telefonica said in a statement that the sale involved a payment of €780 million in cash to complete the sale and a further €70 million later "dependent upon achievement of agreed financial objectives".
Telefonica Ireland will pass to Three, Hutchison Whampoa's subsidiary in the country, and "create a new competitive dynamic in the Irish market", it said.
"This transaction is part of Telefonica's ongoing policy of proactive management of its asset portfolio with the aim of increasing the company's financial flexibility," said the Spanish firm, which announced a debt level of €51.8 billion in March.
"It is expected that this agreement will reduce Telefonica's net debt position by approximately €780 million, accelerating Telefonica's deleveraging process and bringing the company closer to its stated goal to reach a net debt level below €47 billion in 2013."
Hutchison Whampoa is owned by Hong Kong tycoon Li Ka-shing — nicknamed "Superman" for his business prowess — and has operations in over 50 countries.
The port-to-telecoms conglomerate earned a net profit equivalent to $3.37 billion last year.
The Spanish giant has been hit hard by the financial and economic crisis in its home market and is looking for growth in Latin America, from where more than half of its revenues now come, including its biggest market, Brazil.
It has set as its aim for 2013 to improve sales from last year's figure of € 3.298 billion.
Telefonica's shares were down 1.27 percent in early afternoon trading on the Madrid stock exchange. The index was down by 1.81 percent overall in line with other European exchanges, hit by concerns for US financial stimulus and liquidity in China.