Mahinda resigned as prime minister last week, hours after his supporters attacked anti-government protesters, prompting authorities to impose a nationwide curfew and deploy Army troops in the capital.
The post of deputy speaker was left vacant after Ranjith Siyamabalapitiya resigned from the post twice in one month this year.
In the last election, Wickremesinghe's UNP managed to win just one parliamentary seat, leaving him its sole representative in Parliament.
With soaring prices, fuel and food shortages and lengthy power cuts, Sri Lankans have been protesting for weeks, calling for both the Rajapaksas to step down.
Case filed for arrest of former PM Mahinda Rajapaksa, six others in attack on peaceful protesters in Sri Lanka
The personal complaint was lodged before the Colombo Magistrate's Court where attacks on peaceful protesters outside the prime minister's residence and near Galle Face were cited.
Sri Lanka's new PM Wickremesinghe assumes duties, Opposition says his appointment has 'zero regard' for voice of people
Wickremesinghe had been sworn in as the prime minister of Sri Lanka on five occasions before.
President Gotabaya Rajapaksa has ordered an investigation into the violent clashes that killed at least nine people, including Athukorala, while nearly 300 were injured.
Any interim government Ranil forms will have stability issues as each minister would assume he is no less than the PM.
The Fort Magistrate's Court barred them from traveling overseas due to the investigations taking place on the attacks on the GotaGoGama and MynaGoGama peaceful protest sites on Monday.
Lanka's former strongman Mahinda under protection at naval base as army marches on streets of Colombo
Meanwhile, security forces in armoured vehicles patrolled across the country with orders to shoot at sight amid continuing protests at the government's handling of the worst economic crisis.
'Fake and blatantly false': India refutes 'reports' on sending troops to Sri Lanka as talks start to end political impasse
In its first reaction to the situation in Sri Lanka, India on Tuesday said that it is 'fully supportive' of the island nation's democracy, stability and economic recovery.
Airport without planes, debt-laden seaport: China-backed projects testament to Sri Lanka's mismanagement
The centrepiece of the infrastructure drive was a deep seaport on the world's busiest east-west shipping lane, which was meant to spur industrial activity. Instead, it has haemorrhaged money.
Beijing, while watching warily the fast unfolding of events in Sri Lanka, has not yet commented on the resignation of prime minister Mahinda Rajapaksa.
Sri Lanka Opposition fears military intervention as Speaker asks President to reconvene Parliament this week
The anti-government protesters, who have been conducting peaceful demonstrations since March-end, were set upon by a group of pro-Rajapaksa gangs - mostly the grassroot political leadership.
Indian High Commission rejects local social media reports of Mahinda Rajapaksa and family fleeing to India
The whereabouts of Mahinda Rajapaksa is being speculated since his resignation on Monday. It was reported that Mahinda left his office-cum-official residence, Temple Trees, early this morning.