my ($day,$month,$year) = split("/",$date);

I think that code is answering a different question, but you could have answered the OP's one by adding a join.

my $var1 = q{10/02/2009};
my $var2 = join q{}, split m{/}, $var1;
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Another way would be to use tr, for details look in Quote Like Operators;

my $var1 = q{10/02/2009};
( my $var2 = $var1 ) =~ tr{/}{}d;
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I hope this is of interest.

Cheers,

JohnGG

Update: Added my declarations to second code snippet.