The Japanese camera and copier maker said in a statement that funds required for the purchase would reach 23.6 billion Swedish krona, or about 333.7 billion yen (USD 2.8 billion).
The offer is "friendly in nature and the Board of Directors of Axis has decided to recommend Axis's shareholders to accept it", Canon said.
The offer would be launched as soon as Swedish financial authorities and the Stockholm stock exchange give approval, scheduled for early March.
Axis, established in 1984 in Lund, Sweden, reported a net profit of 539 million Swedish krona for the year to December on sales of 5.45 billion Swedish krona.
Canon said in late January that net profit grew 10.5 percent in 2014 owing to the impact of a weak yen and cost cuts as well as strong demand for its office equipment.
Japan's currency has declined sharply against the dollar recently, a plus for exporters as it inflates the value of repatriated overseas income.
Canon and domestic rivals including Sony and Olympus have seen a big drop in sales of their digital imaging products as camera-equipped smartphone sales boom.
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