The ceremony was scheduled to be held on Monday, but President Alvi had refused to administer the oath to the lawmakers, compelling the government to postpone it.
Anti-terrorism court Lahore Judge Natasha Nasim also handed down two-year rigorous imprisonment each to 72 accused persons, including nine juveniles.
Niazi, hand-picked by his party chief Imran Khan, resigned on Thursday after 25 lawmakers of his party moved a resolution of no-confidence motion against him to replace him with party's regional president Sardar Tanveer Ilyas.
Shehbaz, the younger brother of former three-time prime minister Nawaz Sharif, received 174 votes -- two more than the simple majority of 172.
"We will raise voice for Kashmiris brothers and sisters at every forum, diplomatic efforts will be made, they will be provided diplomatic support, we will give them moral support," he added.
Chaudhry, the former information minister, said that the decision was taken in a meeting of the lawmakers of the party ahead of prime minister's elections for which the party has nominated ex-foreign minister Shah Mehmood Qureshi.
The charged PTI supporters, including women and children, showed their solidarity with Khan during the rally that started at 9 pm on Sunday and lasted till 3 am on Monday.
Pakistan's Opposition leader Shehbaz Sharif on Sunday nominated himself for the post of prime minister, while Imran Khan's party threatened to withdraw its lawmakers from Parliament if the former Punjab chief minister was allowed to contest the election for the top post on Monday.
Shehbaz, the 70-year-old younger brother of former three-time prime minister Nawaz Sharif, has served as chief minister of the country's most populous and politically crucial Punjab province thrice.
The change of government in Pakistan after the exit of hawkish Imran Khan and his likely replacement by hard-core realist Shehbaz Sharif may provide a little window of opportunity for the leaders of India and Pakistan to reset their nearly frozen bilateral ties, according to experts.
As the people of Pakistan woke up to a new dawn on Sunday, the details of the gruelling and murky political activities in the preceding day and night have emerged, showing the country may have averted a damning showdown between ousted prime minister Imran Khan and the powerful Army.
Khan, 69, was not present in the lower house at the time of voting. His party lawmakers staged a walkout.
The Pakistan Parliament witnessed multiple adjournments and heated arguments, but the voting on a no-confidence motion against him appeared to be a distant possibility.
The review petition, filed through Dr Babar Awan and Azhar Siddique, named the Pakistan Peoples Party, Pakistan Muslim League-Nawaz, Supreme Court Bar Association, Sindh High Court Bar Association and the Sindh Bar Council as respondents.
The Opposition parties need 172 members in the 342-member house to orchestrate the downfall of Prime Minister Khan.
In his address, 69-year-old Khan also expressed disappointment over the Supreme Court's verdict on the National Assembly deputy speaker's controversial decision on the rejection of no-trust motion against him.
Earlier in five such cases, the 70-year-old radical cleric had already been convicted for 36 years imprisonment.
Pakistan's Supreme Court on Thursday struck down National Assembly Deputy Speaker Qasim Suri's controversial move to dismiss a no-confidence motion against Prime Minister Imran Khan, in a major blow to the cricketer-turned politician who is now likely to face a no-trust vote in parliament after the ruling.
Pakistan's Chief Justice Umar Ata Bandial on Thursday noted that National Assembly deputy speaker Qasim Suri's move to dismiss a no-confidence motion against embattled Prime Minister Imran Khan through a controversial ruling is, prima facie, a violation of article 95 of the constitution as the apex court heard the high-profile case for the fourth day.
The apex court within hours took suo motu notice of it and a five-member bench started hearing the case on Monday.