The 21-year-old joins on a free transfer following Rovers’ relegation to League Two last season.
“I’m happy to be at the club and I’m excited to get started,” he said.
“I’ve been shopping around a few clubs and it’s a massive club with big expectations.
“Hopefully I can do well, bring something to the team and we can achieve what we want to at the club and take them up.
“I’m an attacking full-back, I like to get forward. I like to assist and score goals. I like to do the defending side as well.”
Horton will officially become a Chesterfield player when his contract at Rovers expires on July 1.
As well as Doncaster, Horton has had loan spells at Gainsborough Trinity and Redditch United.
A left-sided player was a priority for the Blues after releasing Alex Whittle and putting Calvin Miller on the transfer list.