The changes were voted through in the early hours of Wednesday after a debate lasting almost nine hours that saw bitter protests by opposition parliamentarians.
After the vote, opposition senators chanted: "Free courts, free Poland!"
As the upper house debated, opposition activists and politicians staged a protest outside the Senate building.
The changes will now go to the Polish president for signing into law.
The amendments, the latest in a raft of moves designed to overhaul the country’s court system, aim to speed up the appointment of a new Supreme Court head to replace Małgorzata Gersdorf.
Opposition MPs have accused the ruling conservative Law and Justice party of undermining democratic norms and trying to stack courts with its own supporters.
Meanwhile, Poland's ruling majority has long argued that some of those responsible for communist-era crimes in Poland were never brought to justice because the country’s court system remained marred by communist holdovers.
The country's prime minister in December published an opinion piece in the Washington Examiner in which he argued that Poland’s judicial system was “deeply flawed” and that the country’s ruling conservatives had been elected with a mandate to overhaul it.
Dispute with Brussels
Poland’s Foreign Minister Jacek Czaputowicz said last month his country would defend its right to reform its justice system amid a dispute with Brussels over a punitive procedure against Warsaw.
The European Commission, the European Union’s executive arm, this month launched a procedure against Warsaw over its overhaul of the Supreme Court, saying that the changes undermined “the principle of judicial independence, including the irremovability of judges”.
The move followed the European Commission last December taking the unprecedented step of triggering Article 7 of the EU Treaty against Poland, stepping up pressure on Warsaw over judicial reforms and potentially paving the way for sanctions being imposed on Poland.
But Poland's governing Law and Justice party, which swept to power in late 2015, has said that sweeping changes were needed to reform an inefficient and sometimes corrupt judicial system, accusing judges of being an elite, self-serving clique often out of touch with the problems of ordinary citizens.