German Chancellor Friedrich Merz's CDU conservatives trailed well behind the AfD, on 18.5 per cent, and the Social Democrats and Greens both cleared the five per cent minimum threshold to enter parliament, according to an exit poll from the ARD broadcaster.
"We have achieved exactly what we wanted to achieve," the 35-year-old Siegmund said after the first exit polls were announced.
"We have made history in this state."
Turnout was about 76 per cent, well above levels typically seen in state elections.
Siegmund is hoping to become the AfD's first premier of one of Germany's 16 federal states and the youngest ever in the role but the exit polls suggest the party has narrowly missed securing an absolute majority in the state parliament in Magdeburg.
Siegmund, who became a political sensation on the campaign trail in Saxony-Anhalt, said he wanted to extend a hand to all parties willing to bring about a fundamental political transformation in the state.
However, the AfD will not bend to other parties' will, he stressed.
The AfD has never participated in a ruling coalition in Germany's 16 states or its federal government, as all other mainstream parties refuse to work with it in a policy known as the "firewall".
Siegmund - who arrived at his polling station on Sunday in his home town of Tangermünde on a Simson, a lightweight moped made in the former East Germany - drew thousands to his campaign rallies and repeatedly cast victory in the state as a first step towards the AfD securing power in federal elections due in 2029.
The federal AfD's co-leader Alice Weidel hailed a "historic" result which had given the party a clear mandate to govern but it was not immediately clear whether it would be able to form a government.
She said the AfD in Saxony-Anhalt will talk to any sensible party with whom it can find common ground on policy positions.
"That is the mandate from the voters; that is what they expect of us," Weidel told broadcaster ARD.
Incumbent state premier Sven Schulze of the conservative CDU congratulated the AfD and acknowledged the result showed it was the strongest party.
He said that "we as the CDU will also have to deal with this result".
If the AfD is unable to rule outright, it could trigger a protracted process of coalition building by mainstream parties who are determined to keep a party under investigation for "right-wing extremism" by Germany's domestic intelligence service out of power.
The AfD has dismissed accusations of extremism as scaremongering and an insult to the party's millions of supporters.
The AfD's program includes plans to push schools and cultural institutions towards more traditional values, curb immigration and overhaul public broadcasting.
with Reuters and AP
