He was 77.
Morgan died Sunday at his home in Danville, a suburb of San Francisco, according to the family spokesman.
The family said Monday that Morgan died from nonspecified polyneuropathy, or nerve damage. In 2015, Morgan was diagnosed with myelodysplastic syndrome, a form of bone cancer, which would lead him to have a bone marrow transplant a year later from his daughter Angela.
"The Reds family is heartbroken," Red CEO Bob Castellini said in a statement. "Joe was a giant in the game and was adored by the fans in this city."
Morgan, a native of Oakland, California, was named National League MVP in 1975 and 1976, leading Cincinnati to World Series titles both years.
Ohio Gov. Mike DeWine eulogized Morgan as "the greatest second baseman of all time" and a "gracious and genuinely nice person."
"He was a player who mastered every detail of the game," DeWine said in a statement. "We saw him play many times with our older children — Pat, Jill, Becky, and John. It was a thrill to watch him!"
Morgan was inducted into baseball's Hall of Fame in 1990 after a 22-season career with the Houston Colt .45s, the Reds, the San Francisco Giants, the Philadelphia Phillies and the Oakland A's.
Morgan, a 10-time All-Star Game selection, was an all-around offensive force, smacking 268 home runs and stealing 689 bases. He also had a keen eye at the plate, forcing pitchers to walk him 1,865 times, which boosted his career on-base percentage to .392.
Morgan was also a wizard on defense, winning five Gold Glove awards as his league's best fielding second baseman.
Major League Baseball Commissioner Rob Manfred on Monday called Morgan the consummate "five-tool player," meaning he could hit for a high batting average, hit for power, run the bases, field his position and throw the ball with authority.
"Joe was a close friend and an advisor to me, and I welcomed his perspective on numerous issues in recent years," Manfred said in a statement. "He was a true gentleman who cared about our game and the values for which it stands."
At just 5-foot-7, Morgan was known as "Little Joe" throughout his career.
"Joe often reminded baseball fans that the player smallest in stature on the field could be the most impactful," Manfred said.
The lineup of Cincinnati's "Big Red Machine" teams was filled with fearsome hitters like Morgan, Pete Rose, Johnny Bench, Tony Pérez and George Foster, as well as defensive stalwarts like Dave Concepción and César Gerónimo.
The 1975 World Series is best known for Carlton Fisk's home run off the left-field foul pole that won Game 6 for the Boston Red Sox. An NBC camera dramatically captured Fisk wildly waving his arms, begging for the ball to stay fair. But it was Morgan who delivered the decisive championship-winning blow, with an RBI single in the ninth inning to break a 3-3 tie in Game 7. The hit brought home teammate Ken Griffey, the father of future Hall of Fame inductee Ken Griffey Jr.
Even after he left Cincinnati, Morgan was productive late into his career. At age 39 in 1982, Morgan finished 16th in National League MVP balloting and ended the season with a dramatic home run that knocked the rival Los Angeles Dodgers out of playoff contention.
After hanging up his cleats, Morgan had a long career in the booth as an analyst for ESPN's "Sunday Night Baseball," teaming up with Jon Miller, radio voice of the Baltimore Orioles and the Giants, from 1990 to 2010.
As a broadcaster, Morgan was known for his old-school view of baseball and his general rejection of the sport's modern analytics — which was a tad ironic, because those new measures painted him as an even a greater player than his Hall of Fame résumé would show.
His highly varied skill set — to draw walks, score runs, steal bases at a high success rate and avoid hitting into ground-ball double plays — didn't jump off a standard box score.
But modern measures greatly value those traits. The database Baseball Reference rated Morgan as the 21st best position player in the sport's history in its contemporary measure, Wins Above Replacement.
"He had a unique ability to explain what was happening on the field to the average fan," DeWine said of Morgan's broadcasting. "He was a master at explaining the 'why' of baseball."
Joe Leonard Morgan was born Sept. 19, 1943, in Bonham, Texas, about 80 miles north of Dallas.
Perhaps overlooked because of his small stature, Morgan didn't draw much attention from college scouts before he signed a free agent contract in late 1961 with the Houston Colt .45s, a franchise that would later be called the Astros.
Morgan posted several productive seasons with Houston, making it to two All-Star Games, and he was second in the National League Rookie of the Year race in 1965.
Then, in one of the worst trades in baseball history, Houston dealt Morgan away in a huge eight-player trade after the 1971 season, which paved the way for Cincinnati's Big Red Machine dominance.
He was fourth in MVP voting in 1972, leading Cincinnati to the National League pennant.
Morgan played the game with a brash style that could occasionally irk opponents. He was also known for flapping his left elbow in the batter's box, a technique to keep the elbow raised.
"Joe wasn't just the best second baseman in baseball history," Bench once said of Morgan. "He was the best player I ever saw and one of the best people I've ever known."
After he retired, Morgan decried the dwindling number of African American players in baseball.
He was also victimized by a bad arrest at Los Angeles International Airport in 1988, when police threw him to the ground and handcuffed him, accusing him of being a drug dealer. Morgan won a six-digit civil verdict against the Los Angeles Police Department.
"The only thing that saved me was a witness standing next to me who had flown on the plane with me. If I don't have his verification, I'm just another Black guy they grabbed and jostled," Morgan told Playboy magazine in 1999.
"At the trial they said they thought I was a drug dealer," he said. "They lied about so many different things."