Merkel's poor showing in September, along with the SPD's insistence on going into opposition, left her with no viable option other than a "Jamaica" coalition, so named because the three parties' colors correspond with the black, yellow and green of Jamaica's flag.
It means the prospective partners will need to overcome huge differences on issues ranging from immigration to European Union reform, tax and environmental protection.
Katrin Goering-Eckhardt, leader of the Greens in parliament, said forming a coalition would not be easy: "It remains difficult but we can at least get started."
A deal brokered last weekend between Merkel's CDU and its conservative Bavarian sister party, the CSU, to cap the number of immigrants is likely to be hard for the Greens to swallow.
Merkel has acknowledged the difficulties ahead but added that "unusual combinations can of course bring the opportunity to find some solutions to things that had seemed unsolvable until now."
"So now we need to put our noses to the grindstone," she said on the campaign trail in Lower Saxony on Thursday.
An SPD-Green coalition has ruled the state for four years, but lost its majority when a Greens lawmaker defected to the CDU, triggering a snap election.
Lower Saxony's incumbent SPD premier Stephan Weil said he would talk to all parties except the AfD about forming a coalition. It was the first time the SPD has been the biggest party in the state since 1998. Turnout was about 63 percent, according to broadcaster ARD — higher than in 2013.
Sunday's win was the first victory for the SPD under Martin Schulz, who was nominated as its leader in January and suffered three state election defeats earlier this year and then the SPD's worst national result in the post-war era in September.