ben_collinsof course it will
All Canon EF and EF-S lenses do
This is an EF-s lens that will fit the rebel ti series aps-c size sensor.
however not all lenses will fit that sensor without cropping.
Canons EF L series are desinged for full frame sensors so if you shoot with a canon 24-70mm L series lens on an aps-c senor like in the ti line there will be a 1.62x crop, making the lens a 38.88mm - 113.4mm
since this lens was designed to cover an aps-c sensor there will be no cropping but it will not cover a full frame sensor.