The 40-year-old Duncan, who was selected as the first overall pick in the 1997 NBA draft, spent his entire career with the Spurs -- an anomaly in a league where players often change teams.
The Spurs reached the playoffs in every one of his 19 seasons.
— San Antonio Spurs (@spurs) July 11, 2016
"Tim Duncan is one of the most dominant players in NBA history," National Basketball Association commissioner Adam Silver said, adding that Duncan's "understated selflessness made him the ultimate teammate."
"For two decades Tim represented the Spurs, the city of San Antonio and the league with passion and class."
Duncan, together with Tony Parker and Manu Ginobili, formed one of the most successful trios in NBA history. They hold the league record for regular season wins (575) and postseason wins (126).
Duncan and Spurs coach Gregg Popovich also formed a dynamic duo, accounting for the most wins ever by a player-coach duo at 1,001.
Duncan, a three-time NBA Finals MVP and a two-time regular season MVP, led San Antonio to titles in 1999, 2003, 2006, 2007 and 2014.
The Spurs posted a 1,072-438 regular-season record since drafting Duncan -- the best 19-year run in league history.
News about Duncan quickly began trending on Twitter, with the hashtag #ThankYouTD taking hold.
"Nineteen seasons. Five rings. One team. #ThankYouTD," the Spurs tweeted on Monday.
He averaged 19 points and 10.8 rebounds per game during his career. But last season's campaign was disrupted by a knee injury and he played in only 61 games.
San Antonio was eliminated in the playoffs this past season by the Oklahoma City Thunder.
Duncan's final game was a 113-99 loss to the Thunder in game six of the Western Conference semi-finals on May 12. In his career finale, he scored 19 points, with five rebounds and a block in 34 minutes.
- Talk of retirement -
At the end of June, Duncan had exercised a $6.4 million player option for next season, but talk of retirement loomed large.
Spanish star Pau Gasol, who during his career has played power forward and center, has reportedly agreed to join San Antonio on a two-year deal worth $30 million, after spending the last two seasons with the Chicago Bulls -- and it now looks like he will help fill the void left by Duncan.
Ginobili, 38, has said he plans to take his time in deciding about playing a 15th season for the Spurs for $2.9 million next season.
He was emotional about Duncan's departure.
"Even tho I knew it was coming, I'm still moved by the news. What a HUGE honor to have played with him for 14 seasons! #ThankYouTD," Ginobili said on Twitter.
Parker said: "Greatest Power Forward Ever! It was an honor to play with you !! #spursfamily."
Kobe Bryant -- who like Duncan won five league titles over a two-decade career with the same team, the Los Angeles Lakers, before retiring -- tweeted: "Congrats TD #19yrs #GoSpursGo."