Kahkonen was claimed off waivers by the Jets on Tuesday, according to Elliotte Friedman of Sportsnet.
Kahkonen was placed on waivers by the Avalanche on Monday.
Kahkonen stopped 16 of 20 shots in Wednesday's 5-2 loss to the Lightning. The fifth goal was an empty-netter in the third period.
Kahkonen will get the starting nod at home versus the Lightning on Wednesday, Evan Rawal of the Denver Gazette reports.
Kahkonen was recalled from his conditioning assignment with AHL Colorado on Tuesday.
Kahkonen was sent to AHL Colorado on a conditioning stint Thursday.
Kahkonen practiced with the Avalanche on Saturday, Aarif Deen of Colorado Hockey Now reports.
Kahkonen (not injured related) will practice with the Avalanche on Saturday.
Kahkonen was claimed off waivers by the Avalanche on Friday, according to Chris Johnston of The Athletic.
Kahkonen was placed on waivers Thursday, according to Elliotte Friedman of Sportsnet.