He was born in the ancient Hungarian noble family Széll de Duka et Szentgyörgyvölgy, that originally hailed from the Vas county, in the western region of the Kingdom of Hungary. His father was József Széll, ispán-regent of the Vas county, and his mother was the noble lady Júlia Bertha de Felsőeőr. Among his illustrious Hungarian noble ancestors were his maternal grandfather, Ignác Bertha de Felsőeőr, vice-ispán of the Vas county, jurist, landowner, and his maternal great-grandfather, József Sümeghy de Lovász et Szentmargitha, royal counselor, jurist, landowner, and vice-ispán of the Zala county. He studied in Pest and Vienna, and in 1867 became deputy for the district of Szentgotthárd. He very quickly won the reputation of being remarkably well informed on economic and financial questions. Széll was one of Ferenc Deák's confidants, whose ward, the daughter of the Hungarian poet Mihály Vörösmarty, he married. In 1875, he was finance minister in the cabinet of Kálmán Tisza, and as such imposed on himself the task of restoring the shattered credit of Hungary. In 1878 he concluded with Austria the first economic "balancing". At that time, the single Austrian bank was changed, in conformity with this arrangement, into the dualistic Austro-Hungarian bank, and Széll consolidated the Hungarian Rentes, and nearly succeeded in balancing the state finances. As he feared that this balance would again be upset by the occupation of Bosnia and Herzegovina, he resigned from the cabinet, incurring thereby the displeasure of the crown. He still kept his seat in parliament, and as deputy constantly criticized the financial policy of the Tisza cabinet. At the beginning of the 1880s Széll founded the Hungarian Mortgage Credit Bank, of which he was governor until the end of his life. He opened entirely new sources of credit for Hungarian agriculture. He declined repeated offers of the portfolio of finance.
Prime minister
When Dezső Bánffy's ministry suffered a serious crisis at the end of 1898 and was compelled to resign in February 1899, Széll was entrusted with the formation of a new cabinet. By means of the Pact of 23 February 1899, he restored parliamentary peace. On the basis of the so-called Széll formula, a new Ausgleich with Austria until the year 1907 was concluded after long negotiations. The most important result of this was that Hungary attained the status of an independent customs area, but, under the arrangement for reciprocity, still maintained intact the existing conditions of the Customs Union with Austria. In 1901, under Széll's Ministry, the new elections resulted in a Liberal victory, and Prime Minister Széll formed a government. A year later began the struggle for the reform of the national defense, and Széll introduced in 1902 a law for increasing the number of recruits, in exchange for which the Independent Party — under the slogan of "no more soldiers without the introduction of Hungarian as the language service and command" — wanted concessions to the principle of nationality. The obstruction against the provision for defense lasted from the end of January to 4 April 1903, and resulted in the suspension of the constitution. Széll sought to wear down the opposition by delay. As part of the majority would not agree to this, he resigned on 16 June 1903.
Széll married Ilona Vörösmarty, daughter of poet Mihály Vörösmarty on 16 September 1867. They had a daughter, named Ilona. His niece Marianne Csáky-Széll married Czech violinist Jan Kubelík.