The match will be a repeat of the 1986 and 1990 World Cup finals, the first of which was won by Argentina before the then West Germany gained revenge four years later.
Argentina's win compounded the misery for hosts Brazil who were humiliated 7-1 by Germany on Tuesday before seeing their worst fears realised when their South American neighbours booked their place at the Maracana on Sunday.
Midfielder Maxi Rodriguez scored the decisive penalty for Argentina after their goalkeeper Sergio Romero had saved spot kicks from Ron Vlaar and Wesley Sneijder, triggering wild celebrations among Lionel Messi's triumphant team.
"I'm proud to be a part of this group," Messi said in a statement posted on his social media pages.
"They are all phenomenons, what a match they played.
"What madness. We are in the final. Let's enyoy it, it is just a litle step more."
Brazil may have won the World Cup more than any other country, but the one they wanted most of all will now be played between two of their greatest rivals.
For Brazilians, it is unpalatable prospect for the mourning samba nation but for soccer fans, it is a dream showdown between a German team that has wowed everyone at the tournament and Messi, the four-time World Player of the year who has won every honour except the World Cup.
Wednesday's second semi-final in Sao Paulo could not have been more different than Tuesday's goalfest in Belo Horizonte but the sheer tension of the occasion had fans on the edge of their seats.
"I'm very happy because we reached the final and now we will see what we can do," said Argentina coach Alejandro Sabella. "We will give everything as usual, with humility, work and 100 percent effort."
Neither Argentina or the Netherlands created many chances in a dour game that was dominated by defence but ultimately came down to a battle of nerves when they finished deadlocked at 0-0 after extra time.
For players and fans, the tension was almost unbearable and it was the Dutch, who have played in three World Cup finals, including the last one in Johannesburg four years ago, but never won one, who fluffed their lines in the shootout.
It was also a second semi-final defeat on penalties for the Netherlands who suffered the same fate against Brazil in 1998.
"I didn't have the feeling in the second half that we would lose," said Netherlands manager Louis van Gaal.
"And when it comes to penalties you know it's a lottery. The boys did fantastically (well). Nobody had expected this."
The Dutch will play Brazil in the third-place playoff in Brasilia on Saturday as the recriminations into the host nation's limp exit gather pace.
Brazilian media savaged the team's performance with newspapers describing the Germany defeat as an "historic disgrace", "national humiliation", "eternal shame" and a "fiasco".
A lot of the blame was directed at Brazil coach Luiz Felipe Scolari, whose future is now the source of wide speculation with Tite, Muricy Ramalho and Vanderlei Luxemburgo looming as his possible successor.
Brazil President Dilma Rousseff took to social media to express her disappointment to a country reeling from the loss after spending more than $11 billion on hosting the tournament.
"I'm immensely sorry for all of us, our fans and players," she tweeted. "But let's not let ourselves give up. Brazil, get up, dust yourself off and bounce back."
Riot police, who had been deployed at fan sites around the country to handle any violent outbreaks, had a quiet night with most fans too traumatised by the manner of defeat to revolt.
An Argentine journalist was killed in Sao Paulo early on Wednesday morning when his taxi was hit by a stolen car fleeing police. He was the second Argentine reporter to die in a car wreck while covering the World Cup.
The mood in Germany could not have been more different with more than 32 million people watching their country's victory on television, a record rating which accounted for an audience market share of almost 88 percent.
Hundreds of thousands of Germans watched the match from the avenue leading to the Brandenburg Gate and German Chancellor Angela Merkel is expected to attend the final.
Off the field, FIFA suspended the Nigeria Football Federation (NFF) because of government interference.
A regional court in Nigeria last week ordered the sacking of the existing NFF executive after the team's performance at the World Cup, where they were eliminated by France in the second round.
The court appointed a new administrator to run the game in the populous west African nation but FIFA warned Nigeria they would be banned from competing internationally unless the old leadership was restored to power.
"The suspension will be lifted once the court actions have been withdrawn and the properly elected NFF Executive Committee, the NFF general assembly and the NFF administration are able to work without any interference in their affairs," FIFA said.