The two forces sat down to talk on Thursday morning after League ally Silvio Berlusconi essentially gave them the green light by stepping aside on Wednesday night, relinquishing his claim to any cabinet seats for his conservative Forza Italia party.
The League-Forza Italia coalition won the most votes in a March national election at roughly 37 percent.
The anti-corruption Five Stars, which came in second at 32.5 percent, offered to form a government with the League on condition it ditches scandal-tainted Berlusconi, who has been convicted of tax fraud and is a defendant in various trials concerning alleged orgies at his home while he was still prime minister of Italy.
"With today's meeting we have laid the bases to write a government contract between the Five Star Movement and the League," the joint statement said. "It was a very positive meeting, which showed that we are completely on the same wavelength."
The statement added that the two sides agreed on some joint issues, such as rolling back an unpopular pension reform that raised the retirement age, introducing a basic income and a flat tax, cutting the costs of politics, and fighting corruption.
The flat tax is a major pledge by the League, which campaigned under the slogan "More Jobs, More Security, Fewer Taxes, Less Immigration" and which made huge inroads in the wealthier, more industrialized North.
A basic income for all is the flagship pledge of the Five Star Movement, which made massive gains in the chronically impoverished South, where unemployment is three times the national rate of around 11 percent.
The two parties may have to work out their differences on the European Union (EU) and foreign policy, as the League is hardline euroskeptic and looks favorably on Russia, while the Five Stars recently took a more pro-euro, pro-NATO stance. However the Five Stars have changed their position on these issues a number of times in the past.
Both parties asked President Sergio Mattarella, whose job is to name a new prime minister following an election, to give them until Sunday to iron out their agreement and come up with a cabinet line-up.
While both League leader Matteo Salvini and Five Star chief Luigi Di Maio initially claimed the right to become the next prime minister of Italy, both appear to have stepped back from that position.
The consensus among political observers for now is that the premiership might go to a "third figure" respected by both parties. Names being aired include leading economist Carlo Cottarelli, and Salvini right-hand man Giancarlo Giorgetti, who is the League whip in the Lower House and who was the middle man in the negotiations between the two sides.
This means Salvini and Di Maio may reserve key cabinet posts for themselves, such as the interior and the foreign ministries.
Berlusconi's sideways move unblocked a stall that had lasted for over two months, prompting Mattarella on Monday to give the deadlocked parties two options: either the naming of a "politically neutral" executive to steer the country through Dec. 31, or a return to the voting booth this year.
It seems both those options have been ruled out for now. It remains to be seen whether the Five Stars and the League will give rise to a functional government in the coming days.