Alexei Ulyukayev, the ex-economy minister, was accused of trying to extort a bribe from Russian oil major Rosneft, an allegation he denies. He is currently under house arrest.
Oreshkin, his 34-year-old replacement, joined the finance ministry in 2013 as the head of the strategic planning department and became a deputy finance minister in March 2015.
He was not on a shortlist of candidates being circulated by Russian state media.
Putin, who has fired a raft of officials this year to make way for a new generation, praised Oreshkin as a young and efficient expert.
Oreshkin told Putin his main task for 2017 was to find measures to spur economic growth.
"Oreshkin is a great expert in macroeconomics. I don't know anyone on the market who would be better than him in macroeconomics," Finance Minister Anton Siluanov said, commenting on his deputy's appointment.
Oreshkin belongs to a group of young economists who joined the government in the past few years. He started his career as an economist at the central bank in 2002. In 2006, he joined Rosbank, the Russian branch of Societe Generale, before moving on to Crédit Agricole Corporate and Investment Bank.