Sanchez won the confidence motion on Friday by 180 votes to 169 with one abstention.
Pedro Sanchez was sworn in as Spain's seventh head of government since its return to democracy in the late 1970s, taking over from veteran conservative Mariano Rajoy who was ousted over a corruption scandal.
An editorial in the influential El Pais newspaper said: "The no-confidence vote will remove Mariano Rajoy as Prime Minister but won't produce greater political stability".
Rajoy is set to be replaced by the opposition Socialist Party and its leader, Pedro Sanchez, who will likely be sworn in over the weekend.
"Our "yes" to Sanchez is a "no" to Rajoy", Mr Tarda said.
Sanchez's victory resulted in the first ouster of a serving Spanish leader by parliament in four decades of democracy.
The bespectacled 63-year-old leader got up and shook hands with Sanchez before leaving the lower house without a word.
It marks a stunning comeback for Sanchez, who was thrown out of the party leadership after two crushing election defeats in 2015 and 2016 but returned to the job past year.
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Rajoy earlier charged that Sanchez and the Socialists could not win at the polls and so sought the no-confidence vote as the only path to power.
The former economics professor and career politician regained the Socialists' leadership past year.
Mr Rajoy became Spain's first sitting prime minister to stand witness in a trial over the corruption cases, believed to have taken place between 1999 and 2005, and many called for him to resign.
His arrival at the prime minister's office represents an astounding comeback for the man who led the Socialists to two crushing general elections defeats in 2015 and 2016, and was forced out by the party apparatus.
Sanchez dialed that back in his speech to parliament on Thursday, saying there was an opportunity for a new understanding on Catalonia although he wanted the region to stay part of Spain. The Spanish constitution states that the party which presents a no-confidence motion must be prepared to govern.
That ruling spelled the end of Rajoy's rule, and Sanchez was keen to portray himself as a fresh start.
He has also said he wants to "build bridges" with Catalonia's new separatist government, headed by Quim Torra, which will take office on Saturday. He may not have had much political pedigree, but Sanchez had an impressive CV behind him.
Sanchez said he meant to call elections before the end of this parliamentary term in 2020, but he didn't say when, and he probably will want to make his mark first with some headline policies before going to the polls. Pablo Iglesias, the leader of the anti-austerity party Podemos, said his group was willing to serve in Sanchez's administration and urged him to form a government with the forces that had backed him.