I always had my issues with より. I think I know what the sentence tells me content-wise, but I can't figure out a proper translation without feeling rather uncomfortable. I used this guide to refresh my knowledge about comparisons with より and also used their literal way of interpreting より.
Here's my attempt at literal translation:
As opposed to last year (=from last years first month to last month), (the tourists) being many, out of (all the years?) until now they/it became the (having) most (tourists (year)).
So, since it is rather obvious from the context that this year has broken the record in tourists/p.a., I think that 今までで refers to "(out of) all years until now" and therefore puts all those years into comparison with 去年去年１月から１２月 (="this year").
However, coordinating these 2 quite big arguments on both sides of より, I feel like I'm missing out on something when constructing a translation which basically just says: "This years tourists were more than any other years tourists.", when there is a phrase like 去年去年１月から１２月 expressing "this year" and two occurrences of "many" (=多きい/多く) representing the tourists.
The latter also gave me some trouble in analysing the components of 今まででいちばん多くなりました. I'm still not entirely sure which way I have to parse this: Is 多く part of the object in "became the year (having) most (tourists)" or is it the subject "most tourists in "they became the most tourists out of all years". I have a tendency towards the first version, since 今までで in this context suggests that "year" could be the subject of なる here, at least in my eyes.