Likewise, Lawrence Gonzi, Malta's prime minister, will withdraw the first euro notes.
The European Commission ruled in May that the two nations had met the strict economic criteria needed to become members of the eurozone, which will now have a population of 320 million.
The commision set an exchange rate of one euro to 0.585274 Cyprus pounds and 0.4293 Maltese lira.
Huge queues extended outside banks across Cypriot capital, Nicosia, last week as people got their first chance to lay their hands on the euro, delivered in high-security convoys.
Cyprus, an island with a population of under one million, joined the EU in May 2004, but a recent survey found 70 per cent of Greek Cypriots believe eurozone membership will lead to inflation and profiteering.
"The euro might be good for big business, but what has the EU done for us? I can only see life becoming more expensive," Anastasia Kolokasides, a housewife said.
The government has promised to monitor the price fluctuations with new legislation to outlaw price-fixing.
Similar fears exist in Malta.
Analysts say adopting a stronger euro can only be good for the Cypriot economy as it will attract more foreign investment, stimulate growth and increase stability as the government will have to abide by stringent fiscal requirements.
Cyprus's key tourism industry attracts a large number of euro-wielding EU citizens, although eurosceptic Britain is the island's largest single market.
Cyprus pounds can still be used in Janurary, but experts believe most will be out of circulation within 15 days with around 600 million pounds worth of notes set to be shredded and 40 million pounds in coins to be melted down.