Elvan received a scholarship from the state-owned mining company Etibank for further study abroad.

He continued his education earning a master's degree in the fields of mining engineering and operations research with a thesis on "Determination of Optimal Production Systems in short-term Mining Production Planning" at University of Leeds, England in 1986.

[2][3][4] Elvan began his professional career in 1987 as an engineer working in the operations research department at Etibank.

[2][5][6][7][8] He assumed as Minister of Finance and Treasury in November 2020 as the successor of Erdogans son in-law Berat Albayrak.

[9] He didn't applaud Erdogans financial policy of low interest rates,[9] resigned from his post on the 2 December 2021 and was succeeded by Nureddin Nebati.