Can I tactfully change my mind after agreeing to do an independent study with a professor?

Do you have a project already lined up ? it sounds like your meeting with the first professor would be to discuss topics for the study. In any case, if no financial agreement has been reached, I see no harm in talking with both professors and then making a decision based on what happens in those meetings. I disagree with @aeismail that you've given a formal commitment at this stage.

You didn't say though why you'd prefer to work with the second professor prior to having a meeting ? is it the subject matter ? general rapport ?

It's a good situation to have to be interested in two projects, and be equally happy to work on either of them.

However, if you have given a commitment to one of the professors, then you really should honor that commitment. Reneging on your commitment will look bad to the first professor, and if the second professor finds out, that could leave a bad impression on his mind, as well.

You could tactfully tell the second professor, "I would really love to work for you, but Professor X gave me an offer first, and I accepted before I received your offer. I am sorry to have to decline, but perhaps we can work together in the future."

I don't think there's a tactful way to say the same thing to a professor after you've made a commitment; you'll come across as very opportunistic instead (note: that's not a good thing!).