CHICAGO—Chicago is embarking on a public-service campaign celebrating and welcoming immigrants to the city, one of the boldest moves yet by a sanctuary city.

The campaign features billboards around the city welcoming immigrants and a new website that points immigrants to city resources, including legal assistance, mental health care and information on how to become a citizen. The website also provides information on Chicago’s municipal identification program, which will be launched at the end of the year and enables all city...