There are more robust ways to do this, but this does what you want.

I changed your filter pattern a bit to make it more robust.

#!/usr/local/bin/perl
use strict; 

my $filter = q{user ([^\s]+) has ([^\n\r]+)$};

my $log_string = "user bob has logged on";
      

$log_string =~  s/$filter/user $1 has accessed the system and is $2/; 

print qq{LINE: [$log_string]\n};
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Outputs

:!./t2.pl
LINE: [user bob has accessed the system and is logged on]
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Wonko