The bill was passed in parliament on Thursday with a quick show of hands by MPs loyal to the president, rather than the usual system of electronic voting.
The changes include a ban on unauthorised tents in public areas and criminal responsibility for slandering government officials.
The move has sparked uproar among the opposition, who say it is illegal.
They have accused the ruling party of a coup.
The US and several EU countries expressed deep concern over the new bills.
As well as signing into law a series of bills, President Yanukovych also fired his long-time chief of staff, Sergiy Lyovochkin, on Friday.
Mr Lyovochkin was rumoured to have wanted to step down after riot police broke up a rally at the end of November – a move that brought tens of thousands of protesters on to the streets the following day.
In a tweet on Thursday following the events in parliament, EU Enlargement Commissioner Stefan Fuele said he was “profoundly concerned by new legislation limiting freedoms”.
He said the move contradicted Ukraine’s “European aspirations” and its commitments in the EU-Ukraine Association Agreement, which President Yanukovych abruptly refused to sign in November, amid Russian economic pressure.
The Ukrainian opposition warned the new measures would further inflame the protest movement, and called for a big gathering in the capital Kiev on Sunday.
Anti-government protesters have been camping out behind extensive barricades in Kiev’s Independence Square – known as the Euromaidan – for nearly two months in the freezing cold.
The mass demonstrations were initially triggered by President Yanukovych’s last-minute rejection of the EU partnership deal.
But the protesters’ demands later widened to include the fight against what they said was widespread government corruption and abuse of power.
On Thursday, MPs from Mr Yanukovych’s Party of the Regions, together with the communists and a number of independents, passed the laws amid scenes of chaos in parliament.
What we’ll have is worse than Belarus”
Iryna BekeshkinaDirector, Democratic Initiatives Foundation
The measures were pushed through in a matter of minutes when lawmakers simply raised their hands, despite the protests of opposition deputies who had earlier blocked the speaker’s platform to try to disrupt the voting.
One of the laws bans any unauthorised installation of tents, stages or amplifiers in public places. Those who violate the law now face a hefty fine or detention.
Another bill provides a punishment of one year of corrective labour for slandering government officials.
Protests involving more than five vehicles in “Automaidan” motorcades were also banned. This followed such demonstrations outside government offices – including Mr Yanukovych’s countryside residence – in recent days.
Party of the Regions MP Oleh Tsariov said the laws aimed to prevent further escalation of the ongoing political crisis.
But the three main opposition leaders described the move as “illegitimate”, saying the pro-presidential MPs had decided to use voting by a show of hands after realising they did not have enough support.
Udar party leader Vitali Klitschko condemned it as a “coup d’etat”, while Arseniy Yatsenyuk, one of the leaders of the Batkivshchyna (Fatherland) party, warned that Ukraine was now bracing for another “wave of protests”.
In Washington, the US state department voiced its “deep concern” that the controversial measures had been passed.
“We believe deeply that the people of Ukraine want to affiliate and want to be associated with Europe and they want to turn in that direction,” Secretary of State John Kerry said.
“And the steps that were taken yesterday are anti-democratic. They’re wrong. They are taking from the people of Ukraine their choice and their opportunity for the future.”
The new laws were also criticised by foreign ministers from Sweden and Poland.
The EU’s ambassador to Ukraine, Jan Tombinsky, said “norms should be adopted through proper procedures, otherwise the credibility of democratic institutions and of the legal system is at stake”.