Ingvar started his career with local club Njarðvík before moving to Stjarnan in the Úrvalsdeild before the 2011 season.[1] With Stjarnan he won the 2014 Úrvalsdeild and was after the season voted by his fellow players the best player of the 2014 Úrvalsdeild.[2] Stjarnan also had a good Europa League run in 2014, advancing past Bangor City, Motherwell and Lech Poznań before losing to Inter Milan in the play-off round.[3]
In 2015, he joined IK Start, but could not secure the first spot in competition with Håkon Opdal. In the summer transfer window, he thus joined Sandnes Ulf on loan.[4]
After one and a half year at Danish club Viborg FF, Jónsson left the club at the end of 2019.[5]
On the 18th of January 2020 it was announced that Ingvar Jónsson would join Víkingur, signing a three-year contract.
International career
Ingvar made his first international appearance on 12 November 2014 in a match against Belgium, when he came on as a substitute for Ögmundur Kristinsson at half-time.[6]