Kjartansson, 25, moved to China in January 2015 after topping the scoring charts in Norway's Tippeligaen with 25 goals in 29 games for Valerenga in 2014.
He was top scorer at Jiangsu Suning too, netting 13 goals in 35 games there, and he also made three appearances for Iceland as they qualified for the finals of Euro 2016, all of them as a substitute.
"I had offers from clubs around Europe but Malmo FF was the most exciting club," Kjartansson said of his decision to sign a deal with the Swedes that will keep him there until the end of the 2018 season.
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Champions in 2013 and 2014, Malmo finished a disappointing fifth in the 2015 Allsvenskan, and coach Age Hareide left to take over the reins of the Danish national team.
Their joy of qualifying for the Champions League group stage for the second year in a row was tempered by finishing bottom of their group as they were hammered 5-0 by Paris Saint Germain and 8-0 by Real Madrid.
(Reporting by Philip O'Connor; Editing by Tom Heneghan)
