King Juan Carlos announced on Monday his intention to abdicate after nearly 40 years on the throne.
Ministers will discuss the steps needed to approve Crown Prince Felipe’s accession to the throne.
King Juan Carlos was seen as popular for much of his reign, but recently many Spaniards have lost confidence in him.
PM Mariano Rajoy said the cabinet meeting would aim at carrying out the “constitutional measures” needed to clear the way for the succession.
The Spanish constitution does not have a precise law regulating abdication and royal succession, and ministers will discuss the special legislation that will be necessary for the process.
The two main parties in parliament remain loyal to the monarchy.
Prince Felipe will become King Felipe VI and will inherit an institution whose reputation has been tarnished by scandals in recent years.
King Juan Carlos, 76, said his son Prince Felipe would “open a new era of hope”
The king announced his decision on Monday in a televised address.
“A new generation must be at the forefront… younger people with new energies,” he said.
Prince Felipe will have to contend with the damage done to the standing of the monarchy by a long-running corruption investigation into the business dealings of his sister and her husband.
Support fell further when it was discovered King Juan Carlos had been on a lavish elephant hunting trip to Botswana in April 2012, in the middle of Spain’s financial crisis.
On Monday evening, thousands of protesters took to the squares of several Spanish towns and cities demanding a referendum on whether the monarchy should continue.
Juan Carlos took the throne in 1975, after the death of General Francisco Franco, the military dictator who had ruled for 36 years.
He became Spain’s first crowned head of state for 44 years.
But he soon ignored Franco’s supporters, who wanted an extension to autocratic rule, and ushered in a new system of parliamentary monarchy.
In later years King Juan Carlos became more of a figurehead.
He has been credited as a stabilizing force for independence-minded areas such as Catalonia and the Basque region.
Prince Felipe and his wife Princess Letizia – a former television presenter – have recently taken on more important roles in ceremonial events.
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