The two leaders, who held an emergency meeting in Paris on Tuesday on the debt crisis -- which is threatening to spread to Italy and Spain -- also called for enforcing strict budgetary discipline by incorporating a "debt brake" in member nations' Constitutions by the middle of next year.
In addition, they suggested imposing a financial transaction tax to curb speculative trade, which could endanger the stability of debt-laden member nations.
The meeting was hurriedly convened in the wake of severe turbulence in financial markets last week and speculation that France may be downgraded from its top-level AAA credit rating by ratings agencies.
Merkel and Sarkozy said the proposed joint economic governance is intended to closely coordinate the financial and economic policies of the 17 nations under the leadership of their heads of state and government, who will meet every six months.
European Council President Herman van Rompuy will chair those meetings.
Germany and France, the euro zone's two largest economies, are determined to defend the euro and carry out their special responsibility, Sarkozy told a joint news conference with Merkel after their two-hour meeting in the Elysee Palace, which is presently undergoing renovation.
Chancellor Merkel said their decisions marked the beginning of a new phase of cooperation for the euro zone.
There should be stronger coordination of economic and financial policies among nations having the single currency, she said.
Until now, the meetings of the euro group were held at the level of finance ministers under the chairmanship of Luxembourg Prime Minister Jean-Claude Juncker. Both leaders rejected calls for introducing euro bonds to help ease the debt burden of some member nations and to calm down nervous markets.
"I don't think that introduction of a common government bond will be helpful to deal with the present euro zone debt crisis," Merkel said.
Sarkozy said he did not think this is the right time to introduce euro bonds. However, he said he can imagine about such bonds some time in the future at the end of a European process of integration, he said.
The two leaders met as European shares ended a three-day rally on Tuesday after the latest German economic data showed that the engine for growth in the euro zone has slowed down, while the euro zone continued to stagnate for the second quarter.
Germany's Federal Statistical Office said the economy grew by just 0.1 per cent in the second quarter compared to the projected 0.5 per cent as a result of a sharp drop in consumer spending and a decline in the construction sector.
Germany and France agreed to introduce a tax from 2013 only for the companies of the two countries to harmonise the methodology for calculation and fixation of tax levels.
What is more, in future, the two nations will deliberate on their annual budgets at joint cabinet meetings before presenting them to their national parliaments.
In Brussels, European Commission President Jose Manuel Barroso and Commissioner for Monetary Affairs Olli Rehn hailed the outcome of the meeting as an important step toward strengthening governance of the euro zone.