Lahore High Court Chief Justice Umar Ata Bandial administered the oath of office to Sarwar.
The post fell vacant with the resignation of Makhdoom Ahmed Mahmood, a nominee of outgoing President Asif Ali Zardari, a few weeks ago.
Sarwar claims to have renounced his British citizenship as a dual national cannot hold a public office in Pakistan.
He belongs to Faisalabad district of Punjab and settled in Britain 35 years ago. He was elected as a Labour MP for Glasgow Govan in 1997 and served till 2010.
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Talking to reporters after his swearing-in, Sarwar said he would work with all political parties for national progress. He also vowed to protect the rights of minorities.
Earlier, Rehman Malik, who was Interior Minister in the previous Pakistan People's Party-led government, had to give up his British nationality to continue in office.
Mubeen Qazi, a Supreme Court lawyer, contended Sarwar had only surrendered his British passport and not his nationality. "Such Pakistani British nationals restore their nationality status by submitting an application with USD 1,000 fee after enjoying political office in Pakistan," Qazi told PTI.
On the other hand, Prime Minister Nawaz Sharif's decision to "import" a former British citizen for the coveted slot has left other contenders disappointed.
PML-N lawmakers Zulifqar Khosa, Rafique Rajwana and Jaffar Iqbal, who had been lobbying for the post, have expressed their disappointment at the leadership's choice.
The Sharif family is facing criticism for appointing handpicked persons to coveted positions like the President and Governor of Punjab. The opposition has described new President Mamnoon Hussain as a "remote controlled" leader.