The only exceptions are to be made by the minister of justice, also a member of Law and Justice.
The revamped Supreme Court would have final appeal powers over all civil and criminal cases.
There is concern that, upon seizing control of the supreme court, PiS will next try to push through a constitutionally controversial election law and have an obedient supreme court rubber-stamp a vote cementing the party's rule.
Also, the president - again, not the justice minister - will also decide which judges may keep their seat in the court when the new law comes into force in 30 days, rather than 14 days as originally planned.
In 2016, Warsaw launched a new inquiry and the investigators claims the president's plane began to break up in the air, and one of the most likely explanations for the crash was thermobaric explosives going off inside the aircraft, an idea both Russian and Polish investigators from the earlier investigations have described as ludicrous. Poland's right-wing government is in trouble because it is interfering with the principle of an independent judiciary, which is considered sacrosanct by the powers that be in Brussels.
The Supreme Court bill still needs approval from the Senate and from Duda, who hails from the ruling party.More news: Court denies bail to actor Dileep
They would put the "judiciary under the full political control of the government" and make "the judges serve at the "pleasure of the political leaders", Jean-Claude Juncker's deputy told reporters".
He said the Commission will "have no doubt" open infringement procedure against Poland next week, and send supplementary rule of law recommendation to Warsaw.
The bill, submitted by the conservative ruling Law and Justice (PiS) party, must now be approved by the upper house.
Politico EU reports that Polish President Andrzej Duda has taken the unusual step, for him, of challenging his party leadership on this issue.
Both houses of parliament last week adopted separate legislation that would give the minister of justice the power to name the chief justices of the European Union member's common courts.
Donald Tusk, European Council President and former Polish prime minister, said the changes are "backward".More news: Trump Today: President says Senate 'must come through' on Obamacare replacement
Since 2015, the PiS has tightened government control over courts and prosecutors, as well as state media. Some carried banners urging Duda to veto the bill. The law gave a simple majority of lawmakers the right to appoint judges to the council.
The current judges could theoretically be reinstated in the revamped court, but there is little likelihood PiS will proceed in that fashion.
Thursday's vote was 235-192 with 23 abstentions after a parliamentary commission summarily rejected 1,300 opposition amendments to it.
The vote in Poland's parliament, which is dominated by the ruling Law and Justice party, was preceded by a heated debate and street protests. It is the latest in a raft of bills that critics say are wiping out judicial independence.
The European Commission has warned it could strip Poland of its European Union voting rights over the changes the government is making to the judiciary.More news: Donald Trump's Climate Change Denial Ignites the Grass Roots