The 64-year-old Dutchman is the first non-Pole to coach Poland's national team. Janas led a disappointing World Cup campaign in Germany and resigned after their first round exit.
"I am happy we managed to persuade such a respected and successful coach," said PZPN chief Michal Listkiewicz of Beenhakker's appointment.
"I believe Beenhakker will introduce a new quality to Polish football and lead us to the European championship finals for the first time."
Beenhakker, who has coached the Netherlands, Saudi Arabia, Real Madrid and Ajax Amsterdam, led Trinidad & Tobago to the World Cup finals for the first time in Germany.
He said: "Poland have a long history of football and several very good results but Poland have never been in the European tournament and this will be a challenge for me."
Poland face World Cup semi-finalists Portugal as well as Belgium, Serbia and Finland in the qualifying group for the 2008 European championship.
Poland's conservative government has pressed publicly for heads to roll at PZPN since the Poles' second exit at the World Cup finals' group stages in four years.
Officials say chief Listkiewicz has engineered Beenhakker's appointment despite opposition from the association's old guard, hoping to head off demands for more radical changes in the game's communist-era infrastructure.
"I don't do anything for my own comfort," Listkiewicz told a news conference. "I just decided the time has come to appoint somebody from the top rank to be our coach. There is no time like the present for making history."