Well, first, for much of history there's been close ties (trade, culture, etc) between Scandinavia and Germany. So Martin Luther's ideas reached Scandinavia relatively quickly.

Second, it came at a very opportune moment in history. Sweden had been uneasy (and de-facto independent for quite a while) in the Kalmar Union that existed between Denmark, Norway and Sweden. In particular there was strife (battles even) between the anti-union Swedish regent Sten Sture and pro-union archbishop Trolle. (two syllables) This lead to the Danish king Christian II invading in 1520, killing Sture in battle and executing his supporters at the Stockholm Bloodbath. This massacre was done under the guise that the anti-unionists were heretics, for having attacked Trolle (and thus the church). Danish Archbishop Didrik Slagheck was present as counsel, although his role has been debated ever since. Swedish archbishop Trolle was also there, having anointed Christian as king of Sweden.

This in turn lead to the successful rebellion lead by Gustav Vasa (and sponsored by the Hanseatic League) against the Danes and making himself king of Sweden in 1523. (To put this in context, Luther nailed his theses to that church door in 1517)

Vasa was a guy who consolidated his power, and in that process did much to consolidate Sweden as a kingdom. If any king would be considered 'father of the nation', it'd be him, which is also a role he'd assigned himself in his own propaganda. (He was so good at propaganda, exaggerated stories about him were reported as fact in schoolbooks well into the late 19th century).

When Vasa became king, Trolle had naturally fled to Denmark a few years earlier as the uprisings were getting started, while - after anger from the Vatican over what'd happened in Stockholm - bishop Slagheck was scapegoated for the massacre and burned at the stake in Copenhagen. But the Vatican still considered Trolle the rightful archbishop of Sweden, and demanded that king Vasa recognize him as such. Which he refused to do, since he naturally considered Trolle a traitor.

So you had Vasa being pressured by Rome to reinstate Trolle, Vasa gathering as much power and wealth as possible, and new ideas coming out of Germany - ideas that'd give Vasa both political power over the church, and its material property. It was a good match. He had started approaching Protestantism already the same year he took the throne, and gradually increased his power over the church during the next decade. There's no single definite date the reformation happened, but relations with Rome were severed completely by 1536, when canon law as abolished.

Finland was part of Sweden until 1809, so it was reformed at the same time.

The Danes themselves revolted against Christian II after Sweden did, and he ended up in exile (and later in prison). But Christian had tried to reform the church, although within a catholic framework, following Erasmus of Rotterdam. These reforms were abolished by his successor Frederik I who took over the same year as Vasa - 1523. During the 1520s, reformation ideas spread in Denmark, and the king was rather passive about it, perhaps because of a fear of angering the populace given what happened to his predecessor. In exile, Christian had converted to Lutheranism, and had started encouraging his countrymen to convert as well. But by the late 1520's, Frederik had started asserting more control over the church as well - closing some monasteries and taking the right to appoint bishops, although the country was still officially Catholic. Seeing as how both his rivals Vasa and Frederik were headed towards Protestantism, Christian converted back to Catholicism.

When Frederick died in 1533, they couldn't immediately agree on a successor, not least complicated by the religious strife that had been building up, which lead to the Count's Feud - a civil war between nobility that'd elected the protestant Christian III and those who'd reinstate the repented-Catholic Christian II. - The Hanseatic League now supporting the latter. Over in Sweden, Vasa wasn't going to sit passive while his old arch enemy attempted to reclaim the throne, and entered the war on the side of Christian III, who ended up winning the war and thus securing Denmark as a Lutheran nation.

Norway remained in a Danish-dominated union with Denmark until 1814, so the reformation, so the reformation began there in 1536 as well.

So to summarize it all: Protestantism reached Scandinavia quite quickly - both before the counter-reformation had gotten started, and also before there was competition from other new groups like Calvinists, and it happened at a point of political unrest.