The swearing-in will automatically bring an end to Madrid's direct rule over the wealthy, northeastern region imposed in October after a failed bid to break from Spain.
"Prime Minister Pedro Sanchez, let's talk, let's address this issue, let's take risks, you and us," Torra said, just minutes after Sanchez himself was sworn in in Madrid.
Sanchez takes office after ousting veteran conservative leader Mariano Rajoy from power in a no-confidence vote on Friday.
"We need to sit down at the same table and negotiate, government to government," Torra said. "This situation we're going through cannot go on for even one more day."
Sanchez, a 46-year-old economist who as opposition leader was sharply critical of Catalonia's secession bid, has promised to try to "build bridges" with the region's new government which is still determined to work towards
Torra's call for talks came as his handpicked 13 councillors took oath in the regional presidency in Barcelona -- some of them wearing yellow, the colour that has come to symbolise the separatist cause.
"Do you promise to faithfully fulfil the duties of the post you're taking on at the service of Catalonia in accordance with the law and with loyalty to Catalonia's regional president?", Torra asked each one.
"Yes I promise," they responded to strong applause.
An empty chair with a yellow ribbon stood in the chamber to represent Catalan separatists who are in jail over their role in last autumn's independence push and those like ousted Catalan leader Carles Puigdemont who
Letters were read out by loved ones of those affected, during a ceremony that saw several onlookers break down in tears.
End of political limbo
The swearing-in ends months of political limbo in the northeastern region after the independence bid last October caused Spain's biggest political crisis in decades.
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.
Spain's central government last month recognised the powers of newly-elected Catalan president Torra but refused to ratify his first choice of councillors because four of them face charges linked to the failed independence drive. The Spanish government called their nomination "a new provocation".
Earlier this week, Torra nominated a new administration which did not include them, prompting Madrid to give its green light. The 55-year-old former editor has been under pressure from some segments of
his own separatist camp to adopt a more conciliatory stance, in order to allow a new Catalan government to take office and end Madrid's direct rule.
Torra was chosen by Puigdemont to be Catalonia's next leader after separatist parties kept their absolute majority in regional elections in December.
The election result was a severe blow to the Spanish government. It had called the polls in the hope of heading off the secessionist push in the region, which is home to around 7.5 million people and is about the size of Belgium.
Puigdemont is currently in Berlin awaiting potential extradition to Spain, where he faces jail on charges of rebellion and misuse of public funds.