No single party has held such a supermajority in Sacramento since 1933.
The Senate seats will be filled in special elections expected in March.
The supermajorities would mark a dramatic shift in Sacramento's balance of power, where GOP legislators have aggressively used their ability to block state budget plans and prevent revenue increases to scale back the scope of state government.
Coupled with the approval of Brown's tax plan, Proposition 30, the Democrats now have not only the power but also the money to break free of the deficit that has paralyzed state government for years.
The pressure on Democrats to restore funding for the many services slashed to balance the budget in recent years will be intense.
Already, activists are pressing lawmakers to pump new money into such programs as college scholarships, dental care for the needy and, of course, public schools.
But the first move Brown and legislative leaders made Wednesday was to reassure voters that they would show restraint.
They promised there would be no frenzy of tax hikes.
"Voters have trusted the elected representatives, maybe even trusted me to some extent, and now we've got to meet that trust," Brown said at a Wednesday news conference in the Capitol. "We've got to make sure over the next few years that we pay our bills, we invest in the right programs, but we don't go on any spending binges."
Still, lawmakers can appear to hold the line on revenue generation without actually doing so.
Supermajorities allow lawmakers to impose new fees to pay for infrastructure and other programs that are not technically defined as taxes.
And the same Democrats who are talking tough about fiscal responsibility this week have for years been touting the programs they want to restore or start once the opportunity is there.
In addition to raising revenue, they would also be empowered to bring constitutional changes and other measures to voters without any GOP signoff -- and to override gubernatorial vetoes.
Given a supermajority, "We're going to use it," Senate President Darrell Steinberg (D-Sacramento) said Wednesday.
"It will be an awesome responsibility," Steinberg said. "But it's very exciting.''
Steinberg briefed the media on his desire to overhaul the tax code.
The result, he acknowledged, could be more money for the state budget.