Sources with knowledge of the deal told ESPN.com that Fesenko ultimately passed on a multiyear offer from the Houston Rockets on Sunday and will soon sign his one-year qualifying offer with Utah worth just over $1 million.
Luxury-tax concerns prevented Utah from offering Fesenko more, but bringing Fesenko back was a high priority for the Jazz with big man Mehmet Okur sidelined indefinitely as he recovers from heel surgery.
Had Fesenko signed an offer with another team, Utah would have had seven days to match. The 7-foot-1 Ukranian is expected to join the Jazz on Monday when they hold their annual media day.
Although Houston offered a longer deal, Fesenko ultimately decided to take the one-year deal with the Jazz, which sets him up to be an unrestricted free agent next summer.
Sources say that the Rockets, meanwhile, have renewed their pursuit of free-agent center Erick Dampier, who remains available after a brief flirtation with the Miami Heat and is also being courted by the Milwaukee Bucks.
Marc Stein is a senior NBA writer for ESPN.com