Lawmakers in the upper chamber of parliament, the Council of States, approved the measures expected to cost each bank $90 billion in a preliminary vote late on Tuesday and were due to cast a final vote on Thursday.
The measures would require the banks to hike their high-quality core common equity – which can be converted into cash quickly – to 10 percent of assets, plus hold another nine percent in bonds that could be converted if needed.
The measures are considerably tougher than the Basel III international standards under which banks are to raise their high-quality core common equity to 7.0 percent of assets from the current 2.0 percent.
UBS has criticised the measures which it says will put it at a competitive disadvantage.
Credit Suisse meanwhile has voiced support for the regulations, with its chief executive Brady Dougan declaring that the bank is an "early adopter" of more stringent rules.
In February, the bank raised $6 billion by issuing convertible bonds to Qatar Holding and Saudi Arabia's Olayan Group, in order to get ahead with meeting the new capital requirements.
"The capital requirements are strict but will be achievable for the bank," a Credit Suisse spokesman said on Wednesday.
The lower house of parliament will not take up the government-proposed bill until after the summer break, according to a spokesman.
The measures were proposed by experts last year after a government rescue of UBS during the 2008 global financial crisis.
Last year, a commission of experts advised the government to adopt measures tougher than the Basel III standards as Credit Suisse and UBS are regarded as "too big too fail" because of their size and influence on the Swiss economy.
Beyond tougher capital rules, the government also wants oversight on the remuneration policies of large banks that have had to be bailed out using federal funds.
Under the proposed bill, banks which require state aid could be subject to adjustments on their wage policies, including a complete ban on bonuses or other forms of variable remuneration.
UBS had to be shored up during the financial crisis by a multi-billion dollar state rescue package.
The measures would also require the two banks to keep a 30-day liquidity reserve on hand in case markets seize up, as happened during the financial crisis, and prove they would be able to keep vital services running in case of bankruptcy.
If the banks were to take state aid in the future, they would not be able to pay bonuses without government approval.
The Swiss central bank estimated last year the measures, which would come into force by 2019, would cost each bank around 76 billion Swiss francs ($90 billion).
"The new regulations are not excessive," the central bank's Vice President Thomas Jordan said in an interview with the Neue Zuercher Zeitung last month.
"I am convinced that the competitiveness of Swiss banks is not being threatened," he added.
In Britain, finance minister George Osborne was expected to endorse on Wednesday a call for British banks to ring-fence their retail business from their investment arms to avoid another financial crisis.
UBS shares closed 1.62 percent lower and Credit Suisse was off 0.96 percent while the broader stockmarket finished down 0.92 percent.