Here's some of my research on the world's northernmost tornadoes.
To start, I'll get the obvious out of the way: the northernmost F5 is the 2007 Elie tornado. The northernmost (official) F4 hit Kiuruvesi, Finland on July 11, 1934. Haven't done extensive research on what the northernmost F3 is, but it's likely the Pulkkila, Finland tornado that struck the town on the same day as the Kiuruvesi event.
Now, here is what I believe to be the only significant (F2+) touchdown ever recorded in the Arctic Circle:
This F2 tornado carved an impressively long 27.7 km (17.2 mi) path near Svetlogorsk in the Krasnoyarsk Krai on July 15, 2007. Svetlogorsk itself is 50 kilometers north of the Circle; to the right is Svetlogorsk Airport which is about 10 km SSE of town. The tornado's path is clearly visible to the left of the airport.
On to tornadoes in general. This 1976 tornado near Kiana, Alaska that occurred 29 miles north of the Arctic Circle is commonly cited as the northernmost ever recorded:
While the Kiana tornado is definitely the northernmost confirmed tornado in the United States and North America, there are a few events elsewhere (including the Svetlogorsk F2) that actually beat it. This tornado touched down near Kandalaksha, Russia in 2010, roughly 40 miles north of the Circle.
The Kandalaksha event was itself beaten by another tornado that touched down near Olenegorsk a few years later, about 100 miles north of the Circle.
This is the world's northernmost definitive tornado that can be confirmed per the ESWD: an F1 touched down near Tana Bru, Norway on September 26, 2005. It destroyed an attached garage, moved a trailer and blew (tin?) roofing material for hundreds of meters. The report cites the Ságat newspaper, and unfortunately I don't think the article is available online, but the ESWD as such lists it as "report confirmed by reliable source".
But, what about even further north? There are two more reports in the ESWD database, both on July 10, 2005 also in Finnmark County, Norway. These possible tornadoes touched down near Kjæs and Kåfjord (Nordkapp) a whopping 285 and 300 miles north of the Circle, respectively. The Kjæs tornado reportedly overturned a camping trailer at F1 intensity, but the nature of damage (if any) from the Kåfjord tornado is unknown. Also, these events are listed as "plausibility check passed" rather than "confirmed by reliable source" and the sources cited by the ESWD no longer exist, so the exact nature of these mysterious events is unknown.