Two other bills on a key judicial body and on regular courts also await Duda's signature.
The U.S. State Department sounded an alarm about the legislation, warning in a Friday statement that the bill appeared "to undermine judicial independence and weaken the rule of law in Poland".
The ruling Law and Justice party (PiS) has rushed through its systemic overhaul of the top court. Duda has so far followed the ruling party line.The vote was 55-23 with two abstentions.
"We urge all sides to ensure that any judicial reform does not violate Poland's constitution or worldwide legal obligations and respects the principles of judicial independence and separation of powers", it said in a statement.
Poles took to the streets for another protest with parliament set to defy global allies and mass opposition protests by pressing ahead with legislation giving the government more sway over the judiciary.
Even before the Senate voted on the measure, Duda posted a tweet announcing that he'll meet with the president of the Supreme Court, Malgorzata Gersdorf, on Monday at 11 a.m.
The commission also urged the Polish government to put its new laws on hold.
If the PiS government does not back down, Poland could face fines and even a suspension of its voting rights, although other eurosceptic European Union governments, notably Hungary, are likely to veto strict punishments. Poland faces serious worldwide consequences for politicizing courts, though nobody in Brussels wants to "assault" the country, he said when asked if the European Union is likely to impose sanctions.
Szydlo insisted the government will not bow to pressure "from Polish or from foreign defenders of the interest of the elites". Earlier this week it cleared the lower house and will now go to President Andrzej Duda.More news: Here's why Sonakshi Sinha was replaced by Shraddha Kapoor in Haseena Parkar
Critics at home and overseas say the legislation is part of a drift towards authoritarianism by the government, which espouses nationalist rhetoric coupled with left-leaning economic policy.
From a window high up in the building, a former leader of the Senate, Bogdan Borusewicz, called out encouragement to protesters, saying, "You are giving us strength".
"Authorities are tweaking laws to gain control over citizens and curb freedoms", Tusk said in an interview with broadcaster TVN24 on Friday.
Tusk, former Polish prime minister, wrote in a statement Thursday that "Subjecting the court to one ruling party in the way that Law and Justice has proposed it will ruin already strained opinion on Poland's democracy".
A senior aide to Duda, Krzysztof Szczerski, said Tusk should instead focus on explaining Poland's stance in Brussels.
Poland's upper house of Parliament on Saturday passed a sweeping and controversial judicial bill despite massive nationwide protests and the threat of European Union sanctions.
Since being elected in 2015, PiS has sought to tighten government control over the courts, brought prosecutors and state media under direct government control.
Public protests are planned for Thursday evening.