The new prime minister, Ahmadou Al Aminou Lo, formerly served as head of the Senegal branch of the Central Bank of West African States.
Appearing on state television for the announcement of his appointment on Monday, Lo said he wanted to reassure the local private sector and foreign investors even as he acknowledged Senegal's difficult financial position.
"We must all be aware of the state of emergency our country currently finds itself in. In particular, the state of public finances and its impact on the economy," he said.
"Senegal is a safe and reliable country and intends to remain so."
The International Monetary Fund froze Senegal's $US1.8 billion ($A2.5 billion) lending program following the discovery of misreported debt, pushing the country's end-2024 debt level to 132 per cent of its economic output.
Ousmane Sonko, the outgoing prime minister, had opposed any restructuring of the debt, estimated at $US13 billion ($A18) billion, which he said the IMF was advocating, while Faye has been less vocal on the issue.
Faye fired Sonko, the man who helped the president's political rise, on Friday after months of mounting tensions.