EU European Commission head Ursula von der Leyen also hailed the result
Swiss voters on Sunday rejected a bid to slash immigration from the EU, leaving free movement in the heart of Europe intact, and embraced offering paid paternity leave for the first time.
Final results showed that 61.7% of Swiss voters had balked at an initiative to tear up an agreement permitting the free movement of people between Switzerland and the surrounding EU.
The initiative, backed by the populist right-wing Swiss People's Party (SVP) -- Switzerland's largest party -- had been opposed by the government, parliament, unions, employer organizations and all other political parties out of fear it would jeopardize overall relations with the bloc.
SVP's initiative called for Switzerland to revise its constitution to ensure it can handle immigration policy autonomously.
The party, which has built its brand by condemning immigration and EU influence, warned that the wealthy Alpine country was facing "uncontrolled and excessive immigration."
But the government had cautioned that if Switzerland unilaterally voided the free movement accord, a "guillotine" clause will come into force to freeze the entire package of deals with the EU, its largest trading partner.
SVP lawmaker Celine Amaudruz said it was the mention of the guillotine clause that scared people away from the initiative.
"The Swiss people have spoken and sent a clear message: together we have a great future ahead of us," EU Council chief Charles Michel tweeted late on Sunday.
"We welcome the results of the popular vote and look forward to continuing our close cooperation."
EU European Commission head Ursula von der Leyen also hailed the result, saying that it "upholds one of the core pillars of our relationship: the mutual freedom to move, to live and to work in Switzerland and the EU."
The EU had been following the vote with concern. A similar SVP initiative that narrowly passed in 2014 threw Swiss-EU relations into disarray, and it has taken years to mend the damage.
Several other issues were on the ballot on Sunday as part of Switzerland's famous direct democracy system.
More than 60% of ballots cast were in favour of extending parental leave to fathers, hinting at a shift in Switzerland's rather traditional approach to family models and gender roles that saw 14 weeks paid maternity leave introduced only in 2005.
Until now new fathers were legally entitled to take only one day -- the same amount of time granted when moving house.
Calling the time off "holidays" for new fathers, the SVP and other opponents had gathered enough signatures to put the measure passed by parliament in September to a referendum.
With Sunday's vote, paternity leave will, like maternity leave, offer Swiss parents 80% of their salary, up to a ceiling of 196 Swiss francs per day.
Adrian Wuthrich, head of the trade union federation Travailsuisse and a supporter of the paternity leave push, hailed Sunday's result.
New fathers "finally get more time off than they would for a move," he told the RTS public broadcaster, stressing though that two weeks should be seen as a minimum.