"Today I lost my Dad, my best friend and my mentor," Gwynn Jr. tweeted. "I'm gonna miss u so much pops. I'm gonna do everything in my power to continue to ... Make u proud!"
Gwynn had two operations for cancer in his right cheek between August 2010 and February 2012. The second surgery was complicated, with surgeons removing a facial nerve because it was intertwined with a tumor inside his right cheek. They grafted a nerve from Gwynn's neck to help him eventually regain facial movement.
Gwynn had been in and out of the hospital and had spent time in a rehab facility, Boggs said.
"For more than 30 years, Tony Gwynn was a source of universal goodwill in the national pastime, and he will be deeply missed by the many people he touched," Commissioner Bud Selig said.
Fans paid their respects by visiting the statue of Gwynn on a grassy knoll just beyond the outfield at Petco Park.
Gwynn was last with his San Diego State team on March 25 before beginning a leave of absence. His Aztecs rallied around a Gwynn bobblehead doll they would set near the bat rack during games, winning the Mountain West Conference tournament and advancing to the NCAA regionals.
Last week, SDSU announced it was extending Gwynn's contract one season. The Aztecs play at Tony Gwynn Stadium, which was built in the mid-1990s with a $4 million donation by then-Padres owner John Moores.
Gwynn was born in Los Angeles on May 9, 1960, and attended high school in Long Beach.
He was a two-sport star at San Diego State in the late 1970s and early 1980s, playing point guard for the basketball team — he still holds the game, season and career record for assists — and in the outfield on the baseball team.
Gwynn always wanted to play in the NBA, until realizing during his final year at San Diego State that baseball would be the ticket to the pros.
He was drafted by both the Padres (third round) and San Diego Clippers (10th round) on the same day in 1981.
After spending parts of just two seasons in the minor leagues, he made his big league debut on July 19, 1982. Gwynn had two hits that night. After Gwynn hit a double, all-time hits leader Pete Rose, who been trailing the play, said to him: "Hey, kid, what are you trying to do, catch me in one night?"
In a career full of highlights, Gwynn had his 3,000th hit on Aug. 9, 1999, a first-inning single to right field at Montreal's Olympic Stadium.
Gwynn retired after the 2001 season and became a volunteer assistant coach at SDSU in 2002. He took over as head coach after that season.
He and Cal Ripken Jr. — who spent his entire career with the Baltimore Orioles — were inducted into the Hall of Fame in 2007.
"I had no idea that all the things in my career were going to happen," Gwynn said shortly before being inducted. "I sure didn't see it. I just know the good Lord blessed me with ability, blessed me with good eyesight and a good pair of hands, and then I worked at the rest."
Gwynn also is survived by a daughter, Anisha.
Boggs said services were pending.
AP Sports Writer Janie McCauley contributed to this report.
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