Prior to his appointment, Mishustin served as the head of the Federal Tax Service, where he forged a reputation as a skilled technocrat who successfully reformed the country's fiscal system.
Mishustin is largely unknown to the Russian public and had previously showed little political ambition.
He told Russia's parliament that the country must preserve macroeconomic stability, maintain inflation around 4%, and accelerate work on President Vladimir Putin's flagship "national projects" development program, Reuters reported Thursday.
Mishustin's appointment comes after previous prime minister Dmitry Medvedev, along with the entire Russian government, resigned Wednesday to clear the way for reforms that could potentially extend Putin's grip on power after his presidential term ends in 2024.
Putin has proposed constitutional amendments that would effectively strengthen the powers of the prime minister and parliament at the expense of the presidency -- weakening his successor in the process -- but the exact machinations behind the plan remain unclear.
Putin nominated Mishustin for the prime minister's post late Wednesday, and the new appointee is known for his innovative work in bringing tax collection into the digital economy.
Born in 1966, the new prime minister studied systems engineering and later received two PhDs in economics.
Married with three sons, Mishustin is a pianist and hockey player who also sits on the supervisory board of Russia's CSKA hockey club.
He has also been praised by state media, in particular by Margarita Simonyan, the editor-in-chief of Russia's state-run RT network.
"Mishustin -- this is digitalization, clarity, modern professionalism, decency, the elimination of barriers to legitimate activity, innovative solutions, openness to world technology while taking care of proper sovereignty ... hostility to violent power methods -- in short, everything that we need right now," Simonyan tweeted.
Mary Ilyushina reported and wrote from Moscow, Jack Guy wrote from London.