The vote by 464,000 rank-and-file members ends five months of political deadlock since September's election.
Noting that it would be the biggest opposition party now that the SPD has joined the government, the AfD's parliamentary group leader Alice Weidel promised that "the bill will come at the latest in 2021". In her most recent government statement on European policy last week, she said, "We need a new start for Europe".
The SPD will now decide who will fill the six ministerial roles it is entitled to before Mrs Merkel's expected election by parliament on 14 March.
French Finance Minister Bruno Le Maire wrote on Twitter that he had spoken to Mr Scholz and acting finance minister Peter Altmaier, a Merkel ally, by telephone on Sunday morning to discuss giving the euro zone new impetus after the SPD's vote, adding: "Resolved to work closely together!"
That cost her party dearly in last year's election, which saw the anti-immigration Alternative for Germany (AfD) party enter parliament for the first time.
European Commissioner for Economic and Financial Affairs Pierre Moscovici congratulated the SPD for "their responsible and decisive vote" and said Germany was now "ready to engage for a stronger Europe".
The center-left Social Democrats voted overwhelmingly to remain in a coalition with Merkel's conservative bloc, after hard and drawn-out negotiations triggered by September's elections, which saw the rise of a new right-wing force in German politics and raised questions about Merkel's future.
Differences in migration policy contributed to the collapse of weeks-long coalition talks past year among Merkel's CDU, its Bavarian sister party, the pro-business Free Democratic Party (FDP), and the Green party, following federal elections at the end of September.
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Mrs Merkel praised the SPD's decision and said she looked forward to working with them in coalition.
However, he added: 'The new government could be more important for Europe than for the domestic economy as without this agreement it would have been hard, if not impossible, to get any meaningful reform done in the coming months.
Pressure from German President Frank-Walter Steinmeier prompted Schulz to rethink and weeks of haggling between his party and Merkel's bloc resulted in a coalition agreement.
Kevin Kuehnert, head of the SPD's youth wing, said he was disappointed but that the "Jusos" (youth wing) would keep up their criticism, signaling that, after bringing in a flood of new members, they would be a thorn in the leadership's side. In a tweet, they labelled the SPD's decision a "catastrophe" for Germany, promising fierce opposition over the coming four years. Turn-out in the poll was over 78 percent.
Many Social Democrats, particularly on the left, had argued that the party failed to make its mark on the last government and wouldn't benefit from propping up Merkel for another term.
"While the United States are starting a trade war and China is challenge our industrial leadership, we have been unnecessarily self-absorbed", engineering trade union VDMA's managing director Thilo Brodtmann said.
However, the SPD joining the "Grand Coalition" is facing internal opposition by many young and leftist members who are afraid of being further marginalized by the Union.
DANIELA SCHWARZER: Those actors who may lead their own campaigns to become her successors - they are pretty busy with their new jobs.