The home side head into this playoff tie on the back of a comfortable win in Bulgaria, while Iceland saw off the challenge of Romania in Reykjavik.
When Euro 2016 was expanded to 24 teams, Hungary and Iceland were two of the smaller nations to take full advantage, eventually reaching the knockout stages on a rare appearance at a major tournament.
While the teams remain down the international pecking order, they now have another opportunity to mix it with European football's elite after coming through a series of matches to reach Thursday's final.
Hungary only missed out on an automatic place at Euro 2020 after losing to Wales on the final matchday in Group E, a result which left them down in fourth place.
However, their performances in the UEFA Nations League played in their favour, providing them with the chance to see off Bulgaria by a 3-1 scoreline last month.
Meanwhile, finishing in third position behind France and Turkey in their qualification group, as well as being in the top tier of the Nations League, gave Iceland a last-eight fixture against Romania.
Although the Scandinavian minnows had to withstand a second-half fightback from their opponents, they eventually held on to set up the showdown in Budapest.
Hungary are the form team heading into this contest, following wins in Bulgaria and Serbia with an impressive goalless draw in Russia.
Whereas Marco Rossi's have only lost one of their last five matches in all competitions, Iceland have suffered four defeats over the same period.
Despite those setbacks coming against stronger opposition in the form of England, Belgium and Denmark, boss Erik Hamren is yet to discover whether playing at a higher standard will benefit his players during this contest.
The only time that Hungary and Iceland have met in nine years came at Euro 2016 when a 1-1 draw was played out during the group stages.
Hungary form (all competitions): LWLWWD
Iceland form (all competitions): WLLWLL
Rossi must decide whether to include Dominik Szoboszlai in a five-man midfield or allow the Red Bull Salzburg star to feature further forward.
Hamren could name the same Iceland XI which started the win over Romania on October 8.
Hungary possible starting lineup:
Gulacsi; Botka, Lang, At.Szalai; Bese, Kalmar, Nagy, Szoboszlai, Hangya; Ad.Szalai, Konyves
Iceland possible starting lineup:
Halldorsson; Palsson, Arnason, R.Sigurdsson, Magnusson; Gudmundsson, Gunnarsson, Bjarnason, Traustason; G.Sigurdsson, Finnbogason