In 2016 the number of residents aged 15 and over who had immigrant roots rose to a new record of 2.6 million, a three percent rise on the previous year, said the Swiss statistics office.
Around a quarter of the Swiss population do not have Swiss nationality.
However the definition of ‘population with a migration background' includes these foreigners plus naturalized Swiss citizens – except for those born in Switzerland to parents also born here – and Swiss citizens at birth whose parents were born abroad.
On a national level that comprises 37 percent of the resident population.
In a statement, the statistics office said this concept “is increasingly used to replace the simple distinction between citizens (or nationals) and foreign citizens (or non-nationals), which does not take into account whether individuals are themselves immigrants or have an indirect connection to migration through their parents' migration experienced”.
The figures vary wildly depending on the canton. Geneva has the highest number of residents with a migration background, at 64 percent.
Basel-City, Ticino, Neuchâtel and Vaud follow on 40-50 percent, compared with less than 20 percent in cantons including Obwalden, Jura and Uri.
Around a third of people with a migration background have Swiss nationality. Most arrived in Switzerland as immigrants themselves, while a fifth were born here.
Germans and Italians are the two most represented foreign nationalities, followed by Portuguese and French.
Immigration is a hot issue in Switzerland, which attracts thousands more foreigners every year.
The country has extremely strict citizenship rules: children born in Switzerland to foreign parents do not automatically become Swiss, while most foreigners must have 12 years of Swiss residency and prove they are fully integrated in order to be naturalized.
Earlier this year voters approved a plan to allow third generation immigrants to apply for an easier naturalization process.