Verlaci's name also is found under the forms Vërlaci, Verlaçi, Verlaxhi, and Velaxhi. His first name also is written in various forms, including Shevket, as on his gravestone.
In 1922, Verlaci was the biggest landowner of Albania. He was the leader of the Progressive Party, the biggest conservative party in Albania, which firmly opposed any agrarian reform reducing the landowners' property. The Progressive Party included as its members some North Albanian clan chiefs and prominent Muslim landowners.
In late 1922, Ahmed Zogu became engaged to Verlaci's daughter, winning Verlaci's support and the position of Prime Minister.
In early 1924, Zogu was forced to cede his position of Prime Minister to Verlaci, because of a financial scandal and an attempt of assassination in which Zogu was injured. The date of Verlaci's taking the position of Prime Minister is March 5, 1924 (some sources cite other dates in February or March). Verlaci held this position until June 2 (or June 10), and then fled to Italy. During Fan Noli's regime that followed, a special tribunal created by the government condemned Verlaci to death by default along with the confiscation of all property.
When Zogu was enthroned in 1928, he immediately broke his engagement with Verlaci's daughter. So Verlaci became King Zog's mortal enemy.
On April 12, 1939, Verlaci became the Prime Minister of a government of Albania, formed under the Italian occupation. From April 12 through April 16 (until Italy's King Victor Emmanuel III accepted the Albanian crown) Verlaci was the acting Head of State.
Verlaci supported Albania's claim to ethnic Albanian-inhabited areas in Yugoslavia and Greece.
On November 28, 1939 there was an anti-Italian, anti-Fascist and anti-government street demonstration in Tiranë, supported by a strike of industrial and transport workers.
Verlaci remained at the head of the government until December 4 (other sources cite November 10 or December 3), 1941.
He died in 1946 in Zürich and is buried in the Protestant Cemetery, Rome, Italy.