The former Catalan minister is facing a charge of sedition for her involvement and could be sentenced to 15 years behind bars if convicted.
Last month, nine other Catalan officials were given jail sentences of nine to 13 years for sedition.
Ms Ponsati, an economics professor at St Andrews University, had been expected to hand herself in to police last week, but her legal team said there were "glaring contradictions" in the extradition warrant issued for her arrest.
Her lawyer Aamer Anwar said the "rambling" warrant is full of contradictions, asserting it does not explain what criminal offences the Spanish Supreme Court accuses her of.
However, the warrant has been accepted by UK authorities for execution following a clarification from Spain's Supreme Court judge Pablo Llarena.
Ms Ponsati's legal team say she "utterly refutes" the charge of sedition against her, and believes it is a case of "judicially motivated revenge".
After her arrest at St Leonard's police office in Edinburgh on Thursday morning, Ms Ponsati is expected to be transferred to Edinburgh Sheriff Court for a hearing and her legal team will apply for bail.
In a statement on Wednesday, Mr Anwar said: "It is our intention to argue that there can be no guarantee of a right to a fair trial in Spain, where most members of the Catalan government are already in prison or exile.
"If Clara were to be returned to Spain then it is believed that she would be subjected to a show trial where the only possible verdict could be one of guilty.
"We will submit evidence to show that her extradition would be unjust and incompatible with her human rights.
"It is not a crime to vote for independence and the extradition will be opposed robustly. It is Clara's intention to put on trial the Spanish justice system as well to consider citing those politicians who have interfered with due process.
"Clara is once again taking on the might of the Spanish state and remains resolute and determined to fight and believes Spain will never be able to crush the spirit of the Catalan people."