Born in Berlin, the son of an inn-keeper, Wels in 1891 began an apprenticeship as a paper hanger and joined the SPD. From 1895 to 1897 he served in the German Army. From 1906 he worked as a trade union official, party secretary in the Province of Brandenburg and the Vorwärts press committee. In 1912 he was elected to the Reichstag and with the support of August Bebel joined the SPD executive committee the next year. In the German Revolution of 9 November 1918, Wels was a member of the Berlin Workers' council of the SPD and USPD. He was appointed military commander of the city and consequently had to deal with the occupation of the Stadtschloss by revolutionary forces including violent fights with Freikorps units. Upon the election of Friedrich Ebert as Reich President on 11 February 1919 he acted as presiding officer of the SPD and was formally elected chairman, together with Hermann Müller, on 14 June. In 1920, Wels and Carl Legien organised the general strike that helped defeat the right-wing Kapp Putsch, after which Wels enforced the resignation of his party colleague Gustav Noske as Reich Minister of Defence. He argued for the foundation of the Reichsbanner Schwarz-Rot-Gold and the Iron Front paramilitary organisations against the rising extremist forces of the SA, Der Stahlhelm and Rotfrontkämpferbund. From 1923 Wels also became a member of the executive of the Labour and Socialist International. After the 1930 Reichstag election, Wels advocated the toleration of the cabinet of Chancellor Heinrich Brüning, who had lost the support of the DNVP deputies. Even after the Preußenschlag of July 1932 against Otto Braun's government in the Free State of Prussia, he spoke against a general strike, but after the Reichstag election of November 1932 he rejected any negotiations with the new chancellor, Kurt von Schleicher. On 23 March 1933 Wels was the only member of the Reichstag to speak against Adolf Hitler's Enabling Act. The vote took place during the last session of the multiparty Reichstag, on 23 March 1933. Because the Reichstag building had suffered heavy fire damage in February, the March session was held in Berlin's Kroll Opera House. Despite the incipient persecution of opposition politicians and the presence of the SA, he made a courageous speech opposing the Enabling Act, which gave the Reich cabinet the right to pass laws without the consent of the Reichstag for a period of four years. The Social Democrats were inventive and resistant but eventually overpowered by the Nazis. He stated:
"At this historic hour, we German Social Democrats pledge ourselves to the principles of humanity and justice, of freedom and socialism. No Enabling Law can give you the power to destroy ideas which are eternal and indestructible... From this new persecution too German social democracy can draw new strength. We send greetings to the persecuted and oppressed. We greet our friends in the Reich. Their steadfastness and loyalty deserve admiration. The courage with which they maintain their convictions and their unbroken confidence guarantee a brighter future." .
Speaking directly to Hitler, Wels proclaimed,
"You can take our lives and our freedom, but you cannot take our honour. We are defenseless but not honourless."
All 94 SPD members of parliament who were present voted against the act. Using the powers of the Reichstag Fire Decree, the Nazis had detained several SPD deputies, and others had already fled into exile. The Communists had been banned and so could not vote. The rest of the Reichstag voted in favour. However, Nazi intimidation had worked so well that even if all 107 SPD deputies had been present and voted against it, the Enabling Act would have still passed with the required two-thirds majority for a constitutional amendment. The passage of the Enabling Act marked the end of parliamentary democracy in Germany and formed the legal authority for Hitler's dictatorship. Within weeks of the passage of the Enabling Act, the Hitler government banned the SPD, and the other German political parties chose to dissolve to avoid persecution, making the Nazi Party the only legal political party in Germany. In June 1933, Wels went into exile in the Territory of the Saar Basin, which at the time was under League of Nations control. In August 1933, he was deprived of his citizenship. He then worked to build the expatriate SPD, first in Prague, then in Paris, where he died in 1939.