Hoffman, 42, achieved his milestone in Tuesday's 4-2 home victory over the St. Louis Cardinals.
"It's hard to describe this moment," Hoffman told reporters after team mates mobbed him followed by his wife and three sons.
Hoffman had allowed the children to skip school in California in anticipation of the moment.
"Family is everything," he said.
The accomplishment enabled Hoffman to finally put behind him a season that had looked destined to end in frustration.
He failed to convert on five of his first 10 save chances and lost his position as the team's closer.
"So it became more of a battle of attrition to get there and have that banner turn over (to 600)," Hoffman told Major League Baseball's official website (www.mlb.com).
"Some things aren't easy to get," the right-hander said of the experience, which he described as a "life lesson."
A light-hitting shortstop who converted to a pitcher in 1991, Hoffman recorded his first save in 1993 and has been slowly but surely clicking off ground-breaking numbers ever since.
He eclipsed Lee Smith's all-time Major League record with his 479th save in 2006 and reached 500 in 2007 during his 16 seasons with the San Diego Padres
Hoffman joined the Brewers in 2009 and put up All-Star numbers, saving 37 games.
He began 2010 with 591 saves but collected only five through May 7 and went three months without another. He finally reached 599 on August 29.
So when Hoffman entered Tuesday's game in the ninth inning, fans began to applaud and the public address system blared out "Hells Bells" the AC/DC song that has been the pitcher's calling card throughout his career.
When shortstop Craig Counsell safely fielded a game-ending grounder, fans heard the song again.
"It was great because of how much admiration we all have for Trevor," Counsell said.
Yet despite his record, Hoffman (61-75 career won-lost record) could be nearing the end of his career.
The Brewers are expected to decline his $7.5 million option for 2011, the Major League website reported.
(Reporting by Gene Cherry in Raleigh, North Carolina; Editing by Ed Osmond)