The 21-year-old makes the step up to Championship side Cardiff after scoring a club-record 59 goals for Guisborough last season to top the Northern League scoring charts.
Following the announcement, Johnson tweeted: "Dreams can come true!!
"A massive thank you to @guistownfc for last season. Especially Chris Hardy and his coaching staff for helping me turn my career around by giving me the platform to score the 59 goals to get me noticed and back where I've always wanted to be and playing professional football."
Formerly of Hartlepool United and Real Murcia, Johnson is likely to feature in Cardiff's development squad this season.