Christensen, who served as a member of Parliament from 2001 to 2015, will take over from Peter Gæmelke, who had been in the role since 2011.
The appointment was confirmed by Denmark finance minister Nicolai Wammen, with 80% of the gaming and national lottery monopoly owned by the state.
The incoming chairman became minister of taxation in 2011, before spending time as the minister of defence in 2015, until 2016.
Within gaming, Christensen has been chairman of Danish lottery operator Det Danske Klasselotteri since 2018, though has agreed to resign from that position during the second half of 2020.
Christensen said: "I am very proud of the confidence the minister of finance has shown in me and I look forward to contributing to Danske Spil's further journey. Danske Spil has an important social role in continuing to ensure a balanced and responsible gaming market in Denmark.”
Last month, Danske Spil reported a Q1 year-on-year revenue increase of 0.8% to DKK1.23bn ($186.9m).
