Sanchez said on Thursday that one of the priorities of his government would be "rebuilding bridges" with regions and "establishing the foundations that allow us to normalize relations and start a dialogue between the Spanish government and the new government in Catalonia".
Under the terms of emergency legislation brought in to take over the Catalan administration, Madrid must lift direct rule once a Catalan government is fully formed and cabinet members are sworn in.
It took several tense months after the snap elections for the Catalan nationalists to finally get approval for a new regional government, after several failed attempts when Madrid barred jailed candidates or those in self-imposed exile, such as former regional leader Carles Puigdemont, from office.
The members of Catalonia's former government are to be tried on charges including rebellion.
The 46 year-old Sanchez is now the prime minister in waiting.
The Parliament voted 180-169 Friday to replace Rajoy's government with one led by Sanchez.
Unlike the new government in Italy, Sanchez and his party are staunch supporters of the European Union and the shared currency.