Eyigün, who was employed at Istanbul Metropolitan Municipality, Directorate of Rail Systems between 1997-2012, served as the Supervising Engineer responsible for the Projects and Construction of Rail Systems, the deputy director, and then the director.
He served as the Deputy General Director at the General Directorate of Infrastructure Investments under the Ministry of Transportation, Maritime Affairs, and Communication between 2012-2015. During his tenure at GDII, he occupied several roles such as the Sectoral Official in charge of Research and Construction of Urban Rail Systems and Main Railway Line Projects, the Official responsible for the Eurasia Highway Passage Project, as well as Marmaray Construction Operations.
Between 2015-2018, he worked as a teaching assistant at Yalova University, Department of Transportation Engineering.
During the academic year of 2018-2019, he was assigned to Istanbul Ticaret University Department of Civil Engineering as an Assistant Professor.
He was appointed as an Advisor to the Minister at the Ministry of Transportation and Infrastructure on 8 May 2019; and on 19 September 2019, as the General Director of Infrastructure Investments.