Haller, who made 33 appearances for West Germany and scored 13 goals including six in the 1966 World Cup, died at the age of 73 at his home in Augsburg.
"Helmut Haller is one of the outstanding personalities of German Football," said German Football Association president Wolfgang Niersbach.
"His amazing performance, particularly at the 1966 World Cup, are unforgettable.
"We were in contact up until very recently for his work with the Sepp-Herberger-Foundation and his death really saddens us."
Haller represented his country at the 1962, 1966 and 1970 World Cups.
West Germany lost 4-2 to host nation England after extra-time in the final of the 1966 World Cup, while four years later they finished third in Mexico.
At club level, former striker Haller had three different spells at his home-town club of Augsburg either side of an 11-year stint in Italy with Bologna and Juventus.
He won three league titles during his time in Serie A and was voted footballer of the year in Italy in 1964.
One of Haller's former international team-mates, Jurgen Grabowski, said on the German FA website: "When I was allowed to go to the 1966 World Cup as a young player, Helmut Haller was one of the matadors.
"He was a special player and a wonderful person, always willing to help.
"I have got to say that I had the fortune of being able to spend several years with him."
Augsburg paid tribute with a black background to their website and the words of their chairman Peter Bircks.
"Our thoughts are with his family," said Bircks. "Helmut Haller was one of the biggest footballing heroes of post-war times and has defined a generation of football in Augsburg."