The party that grew out of the 1960s and 70s pacifist and anti-nuclear movement previously governed as a junior ally of the Social Democrats from 1998 to 2005 and forms part of 10 state governments.
Merkel, who won re-election with a weakened majority on Sunday, will need two partners to form the next government, allowing the Greens to flex their muscles as potential kingmakers.
Merkel's conservative CDU/CSU block will also have to woo the pro-business Free Democrats (FDP) into what promises to be a quarrelsome three-way coalition.
The prospect of a "Jamaica coalition", named after the parties' colours of black (CDU), yellow (FDP) and green, is unprecedented at the national level and it could take months of coalition wrangling before a government emerges.
Whereas Merkel's conservatives and the FDP are old bedfellows, the Greens have strongly different views on issues from renewable energy and the "dieselgate" scandal to refugee policy.
But after 12 years in opposition, the Greens signalled they are ready to return to the main stage.
"We are prepared to accept the invitation to hold talks," co-leader Cem Ozdemir said at a press conference on Monday, after his party scored 8.9 percent in the election, half a percentage point up on 2013.
Ozdemir, Germany's best-known politician of Turkish origin, listed climate protection, more social equality and a stronger Europe as top priorities but also warned the Greens would not seek a deal at any price.
Bracing for internal battles
The concept of a Jamaica coalition is not wholly untested in Germany.
The conservatives, Greens and Free Democrats have jointly run the northern coastal state of Schleswig-Holstein since May.
A similar coalition ruled the tiny southwestern state of Saarland from 2009, but, ominously, it collapsed in 2012.
Greens co-leader Katrin Goering-Eckardt said she was bracing for "very complicated" coalition talks, but that the Greens could walk into any negotiations "with confidence" after winning 460,000 new voters.
The environmentalists have come a long way since their early beginnings, when long-haired party members handed out flowers in the Bundestag.
Many of the Greens' flagship issues - from advocating for gay rights to the shift away from nuclear energy - have since gone mainstream, costing them voter support in the process.
But Goering-Eckardt said renewed concerns about climate change and traffic pollution helped win back voters.
The Greens - sometimes mocked as the party of cycling urbanites who prefer their wine organic - will now be girding for an internal battle between the "Realos" or realists eager to govern and the hardcore leftwing that will balk at the slightest betrayal of their ideals.
"In any coalition there will have to be compromises," said Winfried Kretschmann, the popular state premier of Baden-Wuerttemberg, the only German state headed by the Greens.
It's not impossible
One of the first campaign pledges the Greens could be asked to water down is their insistence to get fossil fuel-powered cars off the roads by 2030 in the wake of the diesel emissions cheating scandal.
Both the FDP and Merkel's conservatives object to setting an end date for the combustion engine.
The Greens' calls to phase out coal-fired power plants will also likely get pushback from the FDP, which describes renewable energy as only part of the "energy mix of the future".
On the topic of European reforms, tentatively backed by Merkel, the Greens are also likely to butt heads with the FDP, which opposes further eurozone integration.
"The next German government has to have a clear European compass," Ozdemir said, "one that points in a pro-Europe direction and not towards populism".
The potential coalition partners are also at odds on asylum policy. The FDP wants refugees to be sent home as soon at is safe, whereas the Greens want to make it easier for them to bring over their families.
Both however object to a demand by the CSU, Merkel's Bavarian sister party, to set a cap on refugee arrivals.
The Sueddeutsche Zeitung newspaper said in an editorial that the Greens had touched on issues that "many people care about" during their campaign, and called on the three parties to show "courage".
"Yes, Jamaica sounds like a lot of work," it said. "But it's not impossible."