Former Newcastle, Aston Villa and West Ham winger Solano played under Hull boss Nigel Pearson at Leicester.
The Peru international originally agreed a new six-month deal with the Foxes in May but has now opted to follow Pearson to the KC Stadium.
Meanwhile, the Tigers have said that Algeria international forward Kamel Ghilas could join a Turkish club on loan.
Hull have also appointed Mark McGuire as their new chief executive. McGuire has been with Stockport County for the last three years and will look after the administration and business side of the club.
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