"I'm delighted that Keith has agreed to join and I think he'll be an important player for us," Hull boss Peter Taylor told his clubs official website.
"He's a strong, good passing midfield player that I know uses his voice well on the pitch. Keith will be a very handy player to have in the squad.
"He has good experience at Championship level and I understand that it will be difficult for him to leave Wolves as it is such a big club. But we're looking forward to having him here."
Andrews will complete his move to Hull when he returns from holiday on June 13th.