Vernam, a product of the youth academy at Glanford Park, would have been out of contract at the end of the season and able to leave for a compensation fee.
The 16-year-old, along with three other Under-16 players, had been offered a scholarship with Scunthorpe but was the only one of the quartet not to accept it.
"When Derby came in for Charles both he and his father were keen to explore their options, which is understandable," Iron general manager David Beeby told the club's official website.
"They have a really good set-up at Derby and when they had a look around they were keen for the move to happen.
"Charles' contract was due to expire at the end of the season and he could have signed for Derby with the fee set by the new Elite Player Performance Plan compensation which has just come in. We had offered Charles a scholarship last season but he was the only one of four boys not to accept it.
"The club worked hard to try and persuade Charles to stay. While we are disappointed Charles isn't staying with us, we wish him well and hope he becomes a success. We are proud of our involvement in developing him and will watch out with interest on how his career progresses."