Welti was elected Federal President six times, a total exceeded only by Karl Schenk.

He is remembered for unifying the army, overhauling the Federal Constitution of 1874, and opening political doors for the Gotthard Railway.

His grandfather Abraham Welti belonged to both the National Assembly of the Helvetic Republic and the Consulta.

He immediately took a leading role and commented on issues such as the trade agreement with France and a railway line through the Alps.

In the election of the fifth member of the government on 8 December 1866 Welti received in the first ballot 103 of 159 valid votes, taking office on 1 January 1867.

The necessity became especially evident after the Franco-Prussian War of 1871, when the army's weakness was revealed and conflicts of competence with General Hans Herzog.

However, the constitutional draft of 1872, which was decisively influenced by him, narrowly failed referendum earning 50.5% no votes.

He had to accept federalist compromises, but he was able to enforce his most important concern, the unification of law, in the final constitution of 1874.

He guaranteed the federal government a right of supervision and codetermination, since he did not want to leave this project of national importance to the private sector alone.

In 1878, when the company threatened to fail due to increasing costs, it was able to supply additional subsidies in parliament despite fierce opposition.

For the first time in 1862, the repurchase of private railways by the federal government became the subject of debate, but succumbed to the resistance of the circles around Alfred Escher.

After negotiations with the Nordostbahn had failed, the federal government was able to take over in 1890 a large share of the Jura-Simplon-Bahn.

Another reason for Welti's resignation may have been the family tragedy involving daughter-in-law Lydia Welti-Escher, who took her own life on December 12 after she was locked up in a Roman madhouse the year before.