Hull have been chasing Santos for a number of months, but they have been unable to strike a deal with Rovers for the teenager.
But with the 19-year-old out-of-contract at the Memorial Stadium, Hull have been able to agree personal terms with the Sao Paulo-born winger.
Santos is now set to move to the KC Stadium, although a transfer tribunal will decide on the compensation that Rovers are due - as the player is under 23.
Santos began his career in England as a schoolboy with Stoke City, before joining Rovers in 2011. He made his debut for the club in 2012, before becoming a regular in their side last season - which saw them relegated to the Conference.