However, the welcomes were qualified with an insistence that Mr Mikati’s government be one of reform.
French President Emmanuel Macron described the government formation as “an essential step in taking the emergency measures the Lebanese are waiting for to lift the country out of the deep crisis it finds itself in”.
He called on Lebanon's political leaders to stick to reform commitments and unlock much-needed international help.
US State Department spokesman Ned Price was similarly cautious. On Friday he welcomed the agreement to form a Cabinet after weeks of wrangling, but drew attention to the many challenges still facing Lebanon.
He described the new government as “offering hope that urgent action will be taken to address the dire needs and legitimate aspirations of the Lebanese people".
"We urge quick approval by the parliament so that this new government can get to work on concrete reforms to address Lebanon’s deteriorating economic situation.”
Dominic Raab, the UK’s Foreign Secretary, tweeted his support while also stressing that reforms must follow.
“The formation of a new Lebanese government must be followed by implementation of urgent reforms, a transparent conclusion of the investigation into the tragic Beirut explosion and timely elections next year,” he wrote.
“The UK supports Lebanon, but we must see concerted action."
The EU’s foreign policy chief Josep Borrell also welcomed the new government but said that it would have to deal with “current economic, financial and social crises, implement long-overdue reforms and prepare for elections in 2022".
In July, the EU formalised a legal framework for sanctions against Lebanese politicians deemed to be blocking government formation and desperately needed reforms. The sanctions are set to be discussed at an EU plenary session this week.
UN Secretary General Antonio Guterres described Mr Mikati's new government as a “very important step”. However, he added that “of course it is not enough".
"There are many other things to be solved, but this was the basic condition for anything else to be possible.”
“I wish that he [Mr Mikati] is able to bring together the different Lebanese communities and the different Lebanese political forces in order to make sure that Lebanon is able to overcome the dramatic situation it faces now,” he said.
The UN's Special Co-ordinator for Lebanon, Joanna Wronecka, tweeted that she was pleased to see a new government but said “swift, courageous moves are now needed in the public interest to get governance and economic reforms under way and to prepare for timely elections".
"It is time to ease the burdens on the people of Lebanon and deliver on their aspirations for a promising future," she said.
With an economic and banking crisis at home, Lebanon has found itself increasingly isolated on the international stage. Long-standing allies and international institutions have been reluctant to inject financial support before seeing concrete evidence of reform.
Mr Mikati, a former telecoms magnate, agreed on a Cabinet line-up with President Michel Aoun on Friday, six weeks after being nominated as prime minister-designate.
Mr Mikati is aware of the international support needed for Lebanon to get out of its current situation. Speaking on Friday, he said he would begin discussions with the International Monetary Fund, as well as the Gulf.
“We can only have excellent relations with Arab countries, and we will ask for support from the Gulf Co-operation Council to put an end to Lebanon’s free fall,” he said.
Secretary General of the Arab League, Ahmed Aboul Gheit, said Lebanese hopes rested on "the formation of the government and the reform steps that it will take to alleviate human and economic burdens on the people".
Egypt said it was "keen to boost the new government for aiding the Lebanese people in building a better future".
It said the government formation was an "important move to end the country's prolonged crisis and restore security and stability".
An economic crisis has crippled Lebanon since October 2019, with almost 80 per cent of the population now living in poverty, according to a recent UN report.