The 21-year-old Portuguese spent the first half of the season on loan at RB Leipzig but only started one league game for the Bundesliga side.
Carvalho started his career with Fulham and scored 11 goals in 40 league appearances before joining Liverpool for £5m in July 2022.
He could make his Tigers debut in Friday’s home game against Norwich.
“There’s certain players who understand the game differently in a number 10 position. Allied to his pace, athleticism, his bravery to take the ball and finish actions are the reasons Liverpool signed him,” Hull boss Liam Rosenior told BBC Radio Humberside.
“He’s really excited and he’s looking forward to the challenge. He’s ready to go on Friday, so there’s a possibility he starts.”
Rosenior also confirmed the club are close to signing goalkeeper Ivor Pandur from Fortuna Sittard.
The 23-year-old Croatian has made 16 appearances in the Dutch top flight this season.
