A key member of the Utah teams that reached the NBA Finals in 1997 and 1998, Hornacek has been working with the coaching staff and players.
But he has neither traveled with the team nor been on the bench during home games, which will change.
Hornacek's promotion was first reported by The Salt Lake Tribune on Thursday, when ex-coach Jerry Sloan announced his resignation.
Sloan's top assistant, Phil Johnson, also resigned, leaving two vacancies on Corbin's staff.
Scott Layden moved up and became Corbin's lead assistant.
The addition of Hornacek means one job remains vacant, although Corbin will wait to add a third assistant because he wants to make sure the move is right and works in the long term, especially with a lockout possible this summer.
Asked about Hornacek's promotion, Corbin said, "He's been great. He's been here. He understands what we're running. The guys know him and he's looking forward to getting a little more responsibility. Hopefully, it will work out for everybody."
A three-man coaching staff means "I have to do more, Scotty will do more and Jeff will pick up some of the slack," Corbin said. "We'll get it worked out."
Kirilenko a no-go
The Jazz will be short-handed Tuesday night when they try to get Corbin his first win in a rematch with Phoenix.
The Suns spoiled Corbin's debut with a 95-83 win Friday at EnergySolutions Arena.
Jazz forward Andrei Kirilenko did not participate in Monday's practice and won't play against the Suns, according to team spokesman Jonathan Rinehart.
Kirilenko left the loss to Phoenix with an ankle injury. He had eight points, five rebounds and two assists in 13 minutes.
The Jazz jumped to a 15-point lead, but the Suns outscored Utah in the second half 51-27.
Meanwhile, Ronnie Price (foot) and Raja Bell (calf) might play against the Suns.
If Bell can play, he will start, meaning C.J. Miles would come off the bench.
Bell is "a veteran guy," Corbin said. "He knows what to expect and how to handle situations. … It makes our bench a little stronger with him starting and [Miles] coming off."