Hornung, born Dec. 23, 1935, in Louisville, Kentucky, was one of only seven players to win the Heisman Trophy and be named NFL MVP by The Associated Press. The others were Lamar Jackson, Cam Newton, Barry Sanders, Marcus Allen, Earl Campbell and O.J. Simpson.
"The entire Pro Football Hall of Fame family mourns the passing of Paul Hornung," said David Baker, the president and CEO of the Hall in Canton, Ohio. "He was an outstanding player and an incredible man. Known as 'The Golden Boy,' Paul was above all a leader to whom the Packers looked for the big plays in the big games -- especially during the team's dynasty years under coach Vince Lombardi in the 1960s.
"We will forever keep his legacy alive to serve as inspiration for future generations. The Hall of Fame flag will be flown at half-staff in Paul's memory."
Hornung won the Heisman in 1956 while playing for a 2-8 Notre Dame team. In becoming the only player to win the award while starring for a losing team, Hornung led the Fighting Irish in passing, rushing, scoring, kickoff returns, punt returns and punting. On defense, he led the team in passes broken up and was second in tackles and interceptions.
Hornung was chosen by the Packers No. 1 overall in the 1957 NFL draft, the first of nine future Hall of Famers selected that year. Hornung -- along with fellow Packers stars Bart Starr, Jim Taylor and Jerry Kramer, as well as innovative coach Lombardi -- went on to lead the struggling franchise to the 1960 NFL title game, a 17-13 loss to the Eagles.
In that 1960 season, the star running back accounted for an NFL-record 176 points -- via touchdowns, field goals and extra points -- a mark that stood for 46 years. Hornung was named a first-team All-Pro that season, an honor he repeated the following year, and the NFL MVP, in leading the Packers to the first of four titles they would win while he was on the team.
"In the middle of the field he may be only slightly better than an average ballplayer," Lombardi once said, "but inside the 20-yard line he is one of the greatest I have ever seen. He smells that goal line."
LaDainian Tomlinson broke Hornung's scoring record in 2006 with 186 points on 31 touchdowns -- although Hornung would point out that his record came in 12 games, while Tomlinson needed 16.
Hornung almost missed the Packers' 1961 title game when he was summoned to duty by the Army, but a call from Lombardi to President John F. Kennedy led to Hornung being granted leave.
Said Kennedy in arranging the leave, "Paul Hornung isn't going to win the war on Sunday, but the football fans of this country deserve the two best teams on the field that day."
Hornung scored 19 points -- then a title-game record -- on one rushing touchdown, three field goals and four PATs in the Packers' 37-0 win over the New York Giants.
"Obviously the Packers have lost another legend," Packers coach Matt LaFleur said Friday. "That's four for the year with him, [Herb] Adderley, Willie Wood and Willie Davis, and so anytime you lose legends like that, it's always a sad day. They're a big reason why the Green Bay Packers are the Green Bay Packers. So just wanted to say our thoughts are with his family."
LaFleur also coached at Notre Dame for a year and became familiar with Hornung's legend there.
"I know of the significance and the impact he had there and obviously the impact that he had on the Packers legacy has been huge," LaFleur said, "so it's always sad when you see those legends pass. It's just a tough day for everybody that knew those guys and just their meaning to this organization."
A pinched nerve in his neck suffered earlier in his career started to slow Hornung. Then a gambling scandal brought his career to a temporary halt: He was suspended for the 1963 season by commissioner Pete Rozelle, who found that Hornung and Detroit Lions star Alex Karras had bet on NFL games and associated with "known hoodlums."
Hornung was reinstated for the 1964 season, but his best years were behind him. He rushed for 299 yards in the Packers' 1965 NFL championship season, then 200 yards in nine games in 1966, when the Packers won the first Super Bowl, although Hornung didn't play in that game.
He was selected by New Orleans in the 1967 expansion draft, a heartbreaking moment for Lombardi. But Hornung never played a game for the Saints, instead retiring. Hornung finished his nine-year career with 760 points on 62 touchdowns, 66 field goals and 190 extra points, leading the NFL in scoring for three seasons, from 1959 to 1961.
"Paul was a friend, and we are deeply saddened to learn of his passing," said National Football Foundation chairman Archie Manning, like Hornung a College Football Hall of Fame member. "I always enjoyed being with him and hearing Lombardi and Packers stories, and he was important an important figure in college football, having left a lasting legacy at Notre Dame. RIP No. 5. Our thoughts and prayers are with you, your family, friends and those you touched during your days in South Bend, Green Bay and your beloved hometown of Louisville."
NFL commissioner Roger Goodell said in a statement that Hornung "thrilled a generation of NFL fans with his versatility, athleticism and personality.'' Goodell added that Hornung was "instrumental in growing the popularity of the Packers and the National Football League.''
After wrapping up a career in which he became the only player in NFL history to score 50 touchdowns and kick 50 field goals and earned inductions into both the Pro and College Football Halls of Fame, he was a frequent face on TV football broadcasts, working for CBS alongside such legends as Lindsey Nelson and Vin Scully.
In July 2016, Hornung sued equipment manufacturer Riddell Inc., saying football helmets he wore during his professional career failed to protect him from brain injury. Hornung suffered multiple concussions with the Packers and had been diagnosed with dementia, the lawsuit said.
Hornung is survived by his wife of 41 years, Angela. Due to coronavirus restrictions, there will be a private funeral mass at St. Louis Bertrand Church in Louisville followed by a private burial. A public celebration of his life will be held at a later date, the Packers said.
ESPN's Rob Demovsky and The Associated Press contributed to this report.