No, it won't. AE-1 is an old Canon mounting system, which was phased out with the introduction of the EF mounting system in 1987. In 2003, Canon introduced an even newer mountain system called EF-S which is in many respects similar to EF. If you want to use an AE-1 lens on an EF or EF-S camera, you'll need an adapter, but if you use such an adapter, you'll lose autofocusing capabilities on the lens. An adapter is a great option if you're ok with manually focusing, though, since AE-1 lenses can often be found at great bargains given that they are no longer natively compatible with recent generations of Canon cameras.
EF-S is the mounting system used by Canon's APS-C (crop) sensor cameras, the first of which was the Canon Digital Rebel in 2003. The EF mounting system, as I said, was introduced in 1987 but is still in use on Canon's full frame sensor cameras like the 5D.
Also, for what it's worth and in case anyone is wondering, EF and EF-S are only one-way compatible. You can mount an EF lens on an EF-S camera, but you cannot natively mount an EF-S lens on an EF camera. That's good news for Rebel and XXD owners, though, because it gives novice users access to a great big *ton* of lenses from both the EF-S and EF lines. With an adapter, further access to the AE-1 line of vintage lenses creates a world of opportunities for Canon hobbyist and prosumer shooters.
Just one caveat for the Canon newbie: new Canon glass can be *expensive*. In many cases, you get what you pay for--Canon lenses are stellar optically and can last several lifetimes if well cared for, but dang, let me tell you, there will come a day when you are tempted by the L series lineup. That glass is pricey. If budgeting is a concern for you, be prepared to do a great deal of research into vintage options and third party lens manufacturers like Tamron and Sigma. The kit lens included with this bundle is a great lens and will do a lot for you, but you probably won't always be happy with 55mm max. Don't say I didn't warn you. :P