In a message posted on the official website of the Spanish presidency, Jose Luis Rodriguez Zapatero, Spain's prime minister, said the main challenge will be to provide Europe with an economy that is "more productive, innovative and more sustainable".
Zapatero said that he was "convinced" that the Lisbon Treaty will make Europe "more efficient and dynamic" and contribute to "make Europeans more united".
One of the aims of the EU's new leadership structure is to give Europe a greater voice on the world stage in talks with major powers like China and the United States.
Under the Lisbon Treaty, Rompuy, Ashton and Jose Manuel Barroso, the European Commission president, are intended to be the EU's public face.
But Spain will still chair important EU ministerial meetings on the economy, the environment and energy during the presidency as well as host several summits.
The summits include one between the bloc and Washington in May which Barack Obama, the US president, is expected to attend.
Jerzy Buzek, president of the European Parliament, said: "The coming six months are extremely important for the implementation of the Lisbon Treaty.
"The Spanish presidency will shape the new model of co-operation between EU institutions and member states under the Lisbon Treaty."
During the Spanish presidency the EU needs to agree on a replacement for the bloc's long-term growth strategy known as the Lisbon Agenda which was supposed to make it the world's most competitive economy by 2010.
A new 10-year growth strategy, dubbed the "2020 strategy," is likely to be adopted in March during a summit of EU leaders.
The unemployment rate in the entire EU rose to 9.3 per cent in October, representing 22.5 million people, from 7.3 per cent during the same time last year, according to EU statistic agency Eurostat.
The jobless rate in individual member states varies from lows of 3.7 per cent in the Netherlands and 4.7 per cent in Austria to highs of 19.3 percent in Spain and 20.9 per cent in Latvia.
As fireworks greeted the New Year, Spain raised the level of its anti-terrorist alert, fearing attacks by Eta, the armed Basque separatist group, during its EU presidency.