Challet was elected to the Federal Council of Switzerland on 12 July 1864 as the first member from the Canton of Geneva. He handed over office on 31 December 1872 after being voted out of office. He was affiliated with the Free Democratic Party of Switzerland. During his time in office he held the following departments:
- Department of Finance (1864 - 1867)
- Department of Posts (1868)
- Department of Finance (1869)
- Department of Posts (1870 - 1872)
- Profile of Jean-Jacques Challet-Venel with election results on the website of the Swiss Federal Council.
- Philippe Chenaux: Jean-Jacques Challet (-Venel) in German, French and Italian in the online Historical Dictionary of Switzerland, 2003-09-16.
Giovanni Battista Pioda
|Member of the Swiss Federal Council
| Succeeded by|