Since 2009, Taavi Veskimägi is CEO of Estonian electricity and gas system operator Elering AS. Previously, Taavi Veskimägi worked as an official at the Ministry of Finance, where he served as the head of the public administration department and as a ministerial advisor. Over the years Taavi Veskimägi has hold many non executive positions in different private and public companies and non governmental organisations including two terms as a board member of ENTSO-E.

From 2003 until 2005 Taavi Veskimägi was the Minister of Finance of the Republic of Estonia. In 2003 Taavi Veskimägi became a member of the Estonian Parliament and leader of the Res Publica parliamentary group before he was appointed Estonian Minister of Finance. He held the position of Vice President of the Parliament from 2005 to 2006 and worked both in the parliamentary financial committee and parliamentary committee of European Union affairs. Until 2007 he was the co-chairman of the Pro Patria and Res Publica Union.

He studied in Pedagogical University of Tallinn, majoring in public administration. He graduated in 1998 as MA in public administration. He completed postgraduate education at Reading University in energy management and MBA at Aalto University in business administration.