Mr Scholz said on Wednesday (early Thursday AEDT) he expected members of the parties would give their blessing to the deal in the next 10 days.
The latter two parties said the agreement would be unveiled on Wednesday afternoon.
If party members sign off on it, the three-way alliance — which has never yet been tried in a German national government — will replace the current “grand coalition” of the country’s traditional big parties.
The Social Democrats have served as the junior partner to Ms Merkel’s centre-right Christian Democrats.
Ms Merkel, who didn’t run for a fifth term, is expected to be succeeded by Mr Scholz, 63, who has been her finance minister and vice chancellor since 2018.
The three would-be governing parties said they hope Parliament would elect Mr Scholz as chancellor in the week beginning December 6.
Before that can happen, the deal requires approval from a ballot of the Greens’ roughly 125,000-strong membership and from conventions of the other two parties.
News of the deal came as Merkel led what was likely to be her last Cabinet meeting.
Mr Scholz presented the 67-year-old, who has led Germany since 2005, with a bouquet of flowers.
The negotiations over the alliance were relatively harmonious and speedy compared to previous coalition talks.
But the political transition, with Merkel as a lame-duck caretaker, has hampered Germany’s response to the latest rise in coronavirus cases.
Few details have emerged from the closed-doors talks, including how the parties will divide up the ministerial portfolios.
The alliance is a potentially uneasy mixture because it brings together two traditionally left-leaning parties with one, the Free Democrats, that has tended to ally with the centre-right.
A preliminary agreement last month indicated Germany would bring forward its deadline for ending the use of coal-fuelled power from 2038 to 2030, while expanding the rollout of renewable energy generation.
At the Free Democrats’ insistence, the prospective partners said they wouldn’t raise taxes or loosen curbs on running up debt, making financing a central issue.
Ms Merkel’s Christian Democrats are currently preoccupied with a leadership contest over who will become their next leader and revive the party’s fortunes after it suffered its worst-ever election result.