Tschudi was a member of the Cantonal Government of Basel-City from 1953 to 1959. He was affiliated to the Social Democratic Party. From 1956, he represented the canton of Basel-City in the Swiss Council of States, until he was elected to the Federal Council of Switzerland on 17 December 1959.
During his time in office he held the Department of Home Affairs and was President of the Confederation twice in 1965 and 1970.
Tschudi handed over office on 31 December 1973.