Mr Amato was premier in 1992-93 and treasury minister in the outgoing government led by Massimo D'Alema - who resigned last week.
The new premier will now face confidence votes in both houses of the Parliament - the Chamber of Deputies and the Senate.
If he fails the confidence vote, President Ciampi could dissolve parliament and call a snap general election a year ahead of schedule - something which the opposition has been clamouring for.
The centre-left coalition, which embraces eight parties, enjoys only a narrow majority in Parliament.
This is the 58th Italian government since World War Two.
Green refusal
Almost immediately after being named by Mr Amato on Tuesday, Edo Ronchi - from the Green Party - refused to serve as minister for European Union relations saying he would prefer to remain at the Ministry of Environment.
However, the post was assigned to Willer Bordon, from the Democrats Party.
The newspaper La Repubblica said the setback "confirms that the path on which the new government sets out is slippery and narrow".
There were reports early on Wednesday saying that the Greens had come up with a replacement for Mr Ronchi, but as the swearing-in ceremony began the post was still vacant.
Forming a government
Mr Amato was asked by President Ciampi to form a government after former Prime Minister Massimo D'Alema stepped down following his four-year old centre-left coalition's disastrous showing in regional elections.
The prime minister formed the new cabinet as fast as possible to overcome the political crisis caused by the departure of Mr D'Alema.
The new government has one fewer minister than the previous government because it combines the industry and foreign trade ministries.
'Dr Subtle'
As prime minister in 1992-93, Mr Amato was dubbed "Dr Subtle" for his finesse in reducing public spending.
He also lived through a currency crisis, which forced him to devalue the lira.
Mr D'Alema, the first former communist to head an Italian government, had been in office for 18 months.
He took over from Romano Prodi, who left Italian politics to become president of the European Commission in Brussels.