The 2004 European Champions host Ukraine at the Olympic Stadium in Athens before travelling to Donetsk for the return four days later with a place in South Africa up for grabs.
"We have reached the end of the road," said the 71-year-old German after Greece's first training session. "It is in these matches where you have to prove that you deserve your prize."
The omens appear to favour an improved Ukraine team who secured their playoff berth ahead of Croatia thanks to a 6-0 win over Andorra in their final Group Six match.
It was Ukraine who were responsible for Greece's failure to reach the last World Cup after they won in Athens to qualify ahead of the Greeks.
Rehhagel, whose team earned their playoff spot by virtue of victories over Latvia and Luxembourg in their final two Group Two qualifiers, are boosted by the return to fitness of striker Angelos Charisteas.
The Nuremberg striker is likely to team up with Theofanis Gekas, the top scorer in qualifying with 10 goals, and Celtic's Giorgos Samaras in a three-pronged attack.
Greece will also be relying heavily on in-form Panathinaikos midfielder Kostas Katsouranis, who is confident Greece will be on the plane to South Africa.
"Two very good teams will be playing but in the end I believe that we will qualify," said the 30-year-old.
"We want a victory and a clean sheet but even if there is a goalless draw in Athens then our hopes are still alive. They are in very good form at the moment but we are optimistic."
Ukraine coach Olexiy Mikhailichenko dropped experienced forward Andriy Voronin from his squad for the tie.
The 30-year-old Liverpool striker has been out of favour since criticising Mikhailichenko in the media after the qualifier against Croatia in October last year.
Mikhailichenko said Ukraine would not travel with the intention of playing safe in the first leg.
"We are going to Greece with the target of winning; for us there is no difference between home and away matches," he said.
"Greece have a good blend of youth and experience and possess a coach who has been in charge for many years and they have a disciplined approach. I believe both teams have a 50-50 chance of qualifying."
Greece (probable): Kostas Chalkias, Loukas Vintra, Sotiris Kyrgiakos, Evangelos Moras, Nikos Spiropoulos; Giorgos Karagounis, Kostas Katsouranis, Alexandros Tziolis; Giorgos Samaras, Theofanis Gekas, Angelos Charisteas
Ukraine (probable): Andriy Pyatov, Vasyl Kobin, Yaroslav Rakytsky, Oleksander Kucher, Olexiy Gay, Sergiy Nazarenko, Ruslan Rotan, Anatoliy Tymoschuk, Evgeniy Hacherydy, Artem Milevskiy, Andriy Shevchenko
