$ cat foo.tmpl
foo: [@-- $foo --@]

$ cat foo.pl
#!/usr/local/bin/perl
use warnings;
use strict;
use diagnostics;

use Text::Template;

my $foo = 'FOO_BAR';

my $template = Text::Template->new(
        DELIMITERS => [ '[@--', '--@]' ],
        TYPE => 'FILE',
        SOURCE => 'foo.tmpl'
        );
print $template->fill_in();

You have a few options:
1) Declare the variable with 'our' instead of 'my'.  That will make it
a global variable in the current package.  Note the danger of this -
if your template changes the variable, it's changed in your perl code
as well.
2) Use a variable in a different package, and pass that package to
your Text::Template fill_in method.  For example, rather than
my $foo = 'FOOBAR';
you'd have:
$TEMPLATE::foo = 'FOOBAR';
and then pass PACKAGE => 'TEMPLATE' as an argument to fill_in
3) Pass a hash ref of values to the fill_in method.  So keep your
my $foo = 'FOOBAR';
and pass HASH => { foo => $foo } as an argument to fill_in