The proposed law won 65.5 percent support across the wealthy alpine nation, final results showed.
Switzerland's police and intelligence agencies have had limited investigative tools compared to other developed countries: phone tapping and email surveillance were previously banned, regardless of the circumstances.
But the new law will change that.
The government insisted it was not aiming to set up a vast data-gathering apparatus, similar to the one developed by the US National Security Agency that came into the public eye in part through former contractor Edward
"This is not generalised surveillance," lawmaker and Christian Democratic Party vice president Yannick Buttet told public broadcaster RTS as results were coming in. "It's letting the intelligence services do their job," he added.
Swiss defence minister Guy Parmelin had said that with the new measures, Switzerland was "leaving the basement and coming up to the ground floor by international standards."
Parmelin insisted the Swiss system was not comparable "to the United States or other major powers", who have struggled to find the right balance between privacy and security.
How it would work
Phone or electronic surveillance of a suspect will only be triggered with approval by a federal court, the defence ministry and the cabinet, according to the law.
Bern has said these measures would be used only a dozen times a year, to monitor only the highest-priority suspects, especially those implicated in terrorism-related cases.
The law was approved by parliament in 2015, but an alliance of opponents, including from the Socialist and Green parties, got enough signatures to force Sunday's referendum.
The poll was part of Switzerland's direct democracy system, in which votes are held on a wide range of national issues four times a year, and even more frequently at regional and municipal levels.
Just 43 percent of voters took part in Sunday's poll, a slightly lower mark than recent referenda when flashpoint issues like immigration were on the ballot.
Cold War spying
Overshadowing the vote was a scandal dating back to 1989 and the dying days of the Cold War, when Swiss citizens learned that the security services had opened files on 900,000 individuals, detailing their political and trade union affiliations.
The revelations sparked outrage in a country where people fiercely guard their privacy, and led to significant curbs on police intelligence measures. But the vote highlighted how public attitudes had shifted, with the law's
proponents invoking the string of recent attacks across Europe -- including in Brussels, Nice and Paris.
Criticising that tactic, Green party lawmaker Lisa Mazzone told RTS that the law's approval was won through "a campaign about fear of attacks."
Rights group Amnesty International said it regretted Sunday's result, arguing that the new law will allow "disproportionate" levels of surveillance and that it posed "a threat... to freedom of expression."
But lawmaker Buttet argued that Switzerland's handcuffed intelligence agencies had become too reliant on help from other nations because they were deprived of using the full range of modern investigative tools. "We were naive," he said.
Separately on Sunday's ballot, a popular initiative calling for a 10-percent rise in retirement benefits was defeated, with 59.4 percent voting against. The government was against the measure, citing the cost.
Sixty-four percent of voters also rejected an ambiguous measure calling for unspecified cuts in the use of natural resources such as lumber and water, which the government also opposed.