Who was the Australian International bowler who took a wicket on the last ball they bowled in Test cricket as well as the last ball they bowled on one day internationals in Australia?

That would be the great Glenn McGrath

Well done Hayden, correct.
Glenn McGrath dismissed Jimmy Anderson when England were dismissed for 147 in the 2nd innings of the 5th test of the 2006/07 Ashes series at the SCG. Anderson was the last batter out and Australia chased down the 45 runs to win by 10 wickets.
On the 11 February 2007 McGrath played his last one day international at the SCG in Australia and he dismissed England wicket keeper Paul Nixon on the last ball of England 50th over.
A month or so later McGrath played a vital role in Australia winning the 2007 World Cup played in the West Indies and retired from international and first class cricket.