The 46-year-old lawyer succeeds Elyes Fakhfakh, who resigned as prime minister earlier this month — but Mechichi was not one of the names proposed by the ruling political parties to President Kais Saied.
In a statement following Saturday's announcement, Mechichi said he would "work to form a government that meets the expectations of all Tunisians".
Tunisia has been praised as a rare success story for democratic transition after the Arab Spring regional uprisings sparked by its 2011 revolution.
But its leaders have struggled to meet the expectations of the Tunisian people and the already fragile economy has been battered by the closure of the country's borders because of the COVID-19 pandemic.
The disease has claimed around 50 lives and infected more than 1,400 people in Tunisia.
As well as being interior minister in the outgoing government, Mechichi has been a counsellor to President Saied, handling legal matters. He has previously been chief of staff at the transport ministry and also served in the social affairs ministry.
He now has a month to form a government.
At that point his choice will be put to a parliamentary vote of confidence and will need an absolute majority to succeed. Failing that, parliament will be dissolved and new elections organised within three months.
In the last elections held in October the Islamist-inspired Ennahdha Party came top but fell far short of a majority and eventually agreed to join a coalition government.
Fakhfakh's resignation on July 15 after less than five months in office threatened fresh political deadlock in the nation as it struggles with the economic fallout of the pandemic.
And it came as a political row deepened with Ennahdha over allegations against Fakhfakh of conflicts of interest.
Relations between the 47-year-old outgoing premier and Ennahdha have been strained since the October legislative elections. Fakhfakh stepped down the same day the party filed a no-confidence motion against him.
Ennahdha had initially nominated an independent for premier but he failed to win the support of parliament, leading the president to name former finance minister Fakhfakh for the post.
Faced with the prospect of fresh elections, Ennahdha eventually agreed to join the coalition government.