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The Economic and Financial Meeting (Ecofin), attended by European finance ministers, takes place at the Royal York Hotel. It is being hosted by the UK's Chancellor of the Exchequer, Gordon Brown.
Mr Brown, fresh from delivering a generally well-received Budget earlier in the week, will welcome the 14 other EU finance ministers on Friday.
On Saturday, they will discuss changes in the labour market and attempts to cut unemployment, which is a serious social problem in France, Germany, Spain and several other EU countries.
On Sunday, Mr Brown will take the ministers on an informal day out to Castle Howard, a stately home in North Yorkshire.
The summit will be an opportunity for the finance ministers to discuss the practical details of EMU, how it will work and how it will affect those countries who will not be participating when it comes into operation next January.
The BBC's Europe Business Correspondent, Jonathan Charles, says the agenda will be wide-ranging: "They will be discussing general technical issues concerning monetary union.
"But there will also be a lot of lobbying about who should get the presidency of the European Central Bank. The French and Dutch both have their own candidates and there is likely to be a heated debate."
He adds: "You can also expect a possible leak about which countries will qualify for membership of EMU. The European Commission's report is not due out until Wednesday but the names may be known before then."
Of the 15 EU countries, three - Britain, Denmark and Sweden - have ruled out joining next year and a fourth, Greece, has failed to meet the convergence criteria necessary to join by a wide margin.
It is expected the remaining 11 members will all be allowed to join, although only Luxembourg and Finland have completely fulfilled the criteria.
However, the most important issue of the setting of the exchange rates between the various currencies and the euro, the single currency that will be introduced, will not be decided until May.
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