The swift action in the wake of the charismatic 43-year old millionaire's win in a vote in the ruling Socialist Party on Wednesday, boosted the forint currency, and means Gyurcsany will be able to take charge of formulating Hungary's 2005 budget.
The budget is due to go to parliament by the end of September.
It also removes any uncertainty in the government of the country, which joined the European Union in May, at a time when a persistently high budget deficit makes the forint vulnerable to speculative attacks.
Medgyessy handed over power to Gyurcsany, who was picked on Wednesday to replace him by the ruling Socialist Party, after a statement in which he said the 43-year old millionaire businessman would deputise for him.
Under Hungarian law, Medgyessy would have had to serve out a 30 day notice period and he will retain the title of prime minister for that period even though he will no longer play an active role.
"Prime Minister Peter Medgyessy does not wish to take part in preparing and making domestic policy decisions in the next 30 days," a statement from his office said.
The quick decision, which many of the investors who hold Hungarian bonds had expected to take months pushed the forint sharply higher. It traded as strong as 247.60 to the euro, up from 249.45 on Thursday.
Gyurcsany has still many questions to answer about how he will reconcile his championing of the poor with the fiscal reality of cutting the budget every year.
Gyurcsany won Wednesday's vote by promising disillusioned Socialists, who rule in a coalition with the smaller Free Democrat party, victory in the 2006 election and announcing he would take the fight to the right of centre Fidesz party. The Socialists' have 20 percent support, their lowest level in five years.
At the same time in order to meet the aim of joining the euro by 2010, Hungary has to cut its budget deficit to 4.6 percent of gross domestic product this year and by 0.5 percentage points every year.
"What is essential that work can start on the (2005) budget," said DZ bank financial analyst Gyorgy Kovacs.
"Markets will react to what is actually in that budget," he said.
So far all Gyurcsany has said is that he will pursue stable economic policies.
Gyurcsany does however look set to keep finance minister Tibor Draskovics, who is seen by the investors who hold billions of dollars worth of the country's bonds, as a guarantor of financial rectitude.