This is not so simple. In a nutshell your family and the local poor take precedence for at least a significant part of your tzedaka budget. Only part (for quantification see below) of your tzedaka budget can go to the needy of Israel if there are many local needy to support.
The justification to support the needy of Israel when not living there comes from the lack of local needy people or, according to some opinions, the fact the needy of Israel are poorer than your local needy.
To look at things positively, once someone makes alyah, she gets the opportunity to shift most of her tzedaka budget to the many needs in Israel.
The Rambam in MT Matnot Aniyim 7:13 establishes tzedaka priorities as follows
A poor person who is one's relative receives priority over all others.
The poor of one's household receive priority over the poor of one's
city. And the poor of one's city receive priority over the poor of
and the Shulchan Aruch in YD 251:3 rules similarly, but adds that the poor of Israel takes precedence on other distant countries
Not only a father or child, but any relative should be given
preference to a stranger; a brother of one's father, to a brother of
one's mother; the poor of his own house to the poor of the city at
large; the poor of his own city to the poor of other cities; and the
poor that dwell in the Holy Land to those that dwell in other lands.
This would suggest that, as long as there are poor in your country, you should support them before supporting the needy of Israel.
However R Hershel Schachter comes to illuminate this ruling (from an interview in Jewish Action here)
The question is what does “precedence” mean? Does it mean you give
everything to the poor people in your family? The commentaries assume
that this is not the case. The Chatam Sofer (II: 233-234) writes that
you give half of your tzedakah money to family and divide the other
half among other poor people.
He mentions other poskim adjust the split of the tzedaka budget going to those with precedence: Aruch Hashulchan: 51%, Chochmat Adam and R Moshe Feinstein 67%, Pitchei Tshuva 75%.
Here is an example following [the 67% opinion]: Assuming I have $1,000
to give to tzedakah, if I have a relative who needs $667, I give it to
him. The maximum is $667; but if he needs less, I give him less. Once
my relatives are taken care of within the amount of $667, I give up to
two-thirds of the remaining money to needy neighbors. And of the
remaining money, I similarly give up to two-thirds to aniyei ircha.
And so on, through the list of priorities.
He also writes explicitly that
For many years, the American community was supporting its own yeshivot
and sending its surplus tzedakah money to Eretz Yisrael. Now we
realize that there is no surplus money and yeshivot in America are
closing. I think that our local yeshivot take precedence over aniyim
in another city. Let other people take care of the aniyim in the other
city until we can support ourselves and educate our children.
Now dinonline, in a survey on priorities in tzedaka writes, based on a Chatam Sofer, that
Many authorities rule that the principle of “local poor come first”
applies only when the financial condition of local poor and poor
elsewhere is equivalent. However, if distant poor are worse off than
local poor, for instance if local poor have enough money for food,
whereas others cannot even pay for basic provisions, then distant poor
take precedence over local poor.
Not everyone agrees (R Moshe Feinstein is one who disagrees). See also points 8 and 10 there.
Now, according to Haaretz, Israel has the highest poverty rate in the West. This is partly due to the fact that a large portion of the population (both haredi men and Arab women) choose not to work for religious and cultural reasons. But this might explain why a larger portion of your tzedaka budget could go to the poor of Eretz Israel.