Seeler spent his 19-year playing career, spanning from 1953 to 1972, with Hamburg and is considered the greatest player in the German club's history.
He also earned 72 caps for West Germany and played in its 1966 FIFA World Cup final defeat to England.
The news of Seeler's death was confirmed by Hamburg, where he also worked as president for three years in the 1990s, in a statement on its official website.
"Uwe stands for everything that characterises a good person: down-to-earthness, loyalty, joie de vivre, plus he was always approachable," said HSV board member Jonas Boldt.
"He is the epitome of HSV. I personally have special memories of our get-together on his last birthday. He talked shop, asked about his HSV, gave me tips and a few sayings.
"We will never forget him and will always cherish him. Now our thoughts and sympathy go out to Uwe's family, to whom we extend our heartfelt condolences."
Seeler scored 507 goals in 587 competitive matches for Hamburg, the club said, and he was made an honorary citizen of the city in 2003.
He was crowned German footballer of the year in 1959-1960, 1963-1964 and 1969-1970, while also winning the German top-flight title in the first of those campaigns.
One of four players to have scored at four separate World Cups, along with Pele, Miroslav Klose and Cristiano Ronaldo, Seeler became just the second honorary captain of the German national team in 1972.
The German Football Association (DFB) paid tribute to the striker, who Hamburg said was survived by wife Ilka as well as three daughters and seven grandchildren.
"Rest in peace Uwe Seeler," the DFB tweeted. "Our honorary captain passed away at the age of 85. Our thoughts and sincere condolences go out to his family and loved ones."
Ruhe in Frieden, Uwe Seeler! 🕊️— Die Mannschaft (@DFB_Team) July 21, 2022
Unser Ehrenspielführer ist im Alter von 85 Jahren verstorben. Unsere Gedanken und unser aufrichtiges Mitgefühl gelten seiner Familie und seinen Angehörigen. pic.twitter.com/4kBOkxus4X