The film's junior novel indicates that the Ugnaught guards removed them:
Two Ugnaughts approached Han, removed the manacles from his wrists,
then stepped away from him. Leia watched the lift descend, carrying
Han down into the central pit. From where Leia stood, only Han’s head
was visible. His gaze never strayed from her.
Which you can see in this scene just before Han is placed into the carbonite chamber.
Interestingly, both the script and the official novelisation disagree, stating that he was firmly bound before being placed into the chamber.
As to the bindings on his upper arms, those were already made of carbonite and hence melted away when Leia unfroze him, according to Steve Sansweet, former Head of Content/Head of Fan Relations for Lucasfilm.
Q. When Han Solo is being put into carbon freeze (The Empire Strikes
Back), his hands are cuffed. When he comes out of the chamber his
hands are up in the air and spread apart. Also, when he is thawed in
Jedi, the bindings are gone. How does this happen?
A. The Ugnaughts remove the bindings on Han's hands before he is lowered
into the chamber. If you watch carefully you should be able to catch
it. The bindings that are on his upper arms are made of carbonite, and
thus melt away when Leia releases Han from his carbonite coffin.
Ask the Lucasfilm Jedi Council - Starwars.com