Breaking or break the habit

Solution 1:

The first, because the habit is presumably broken once and not continuously.

I would also rephrase slightly: "Imagining the ill effects of smoking ultimately led him to break the habit."

Out of interest, using a gerund like this also sounds okay: "Imagining the ill effects of smoking ultimately led to his breaking the habit."

But I would prefer the first.

Solution 2:

I think that it could be legitimately worded two ways depending on usage of "led".

You could use "led" in the transitive, more active sense. Per M-W: "to direct on a course or in a direction."

"(It) led him to quit ..."

You can also use "led" in the intransitive, more passive sense. Again per M-W: "to tend toward or have a result."

"(It) led to him quitting ..."

or alternately "(It) led to his quitting..."

Since the "It" in this sense is some abstract imagining, I think the intransitive use fits a little better, but either would be grammatically correct.