Anderson, only the fourth bowler to achieve the feat, cemented his place in cricket history in the closing stages of the rain-marred third and final Test in Southampton.
Fresh downpours prevented play on the last day until 1515 GMT, meaning the home side, 1-0 up in the series, did not have enough time to force a victory.
But despite the tame end to the contest, all eyes were on Anderson and the 38-year-old did not disappoint, striking with his 14th ball of the day to reach the 600-wicket milestone.
Defying a docile pitch, he produced a rising delivery that moved away from Pakistan captain Azhar Ali, a first-innings century-maker, with England skipper Joe Root holding a head-high catch at first slip.
There was applause and cheers from Anderson’s team-mates, with the nick off the shoulder of Azhar’s bat clearly audible at an empty Ageas Bowl.
With no certainty as to when England’s rescheduled series against Sri Lanka or a Test campaign in India pencilled in for the New Year will take place due to the coronavirus pandemic, there was a chance that Anderson could have been stranded on 599 Test wickets.
The bowler is well past the age at which pacemen of earlier generations retired but is still passionate about the sport.
“I absolutely love it – there is no better feeling than putting the boots on, going out there and doing what I love doing,” he told Sky Sports.
“It felt amazing to get 600 wickets. I went to bed last night not expecting to bowl a ball so credit to the groundstaff, who have worked tirelessly. Even if I didn’t get it today there are worse numbers to be stuck on for a few months (than 599) so I’d have been happy either way.”
Azhar, dismissed for 31 following his first innings 141 not out, was happy to be a part of history.
“At least I will get more air time now because they will show that wicket again and again,” he told the BBC. “Hats off to him (Anderson), he’s a fantastic bowler. He doesn’t give you anything, you have to bring your A-game. He’s still bowling at decent pace, with swing and seam.”
Root paid tribute to Anderson, an international bowler for 17 years, by saying: “For him to stand up and perform at the elite end of Test cricket for such a long period of time is an incredible effort.”
Part-time off-spinner Root dismissed Asad Shafiq to leave Pakistan 172-4 but a draw was agreed not long after the match entered the last hour, with Pakistan 187-4 and Babar Azam 63 not out.
The only men ahead of Anderson in the all-time list of Test wicket-takers are three retired spinners – Sri Lanka’s Muttiah Muralitharan (800), Australia’s Shane Warne (708) and India’s Anil Kumble (619).
Kumble tweeted: “Congratulations @jimmy9 on your 600 wickets! Massive effort from a great fast bowler. Welcome to the club.”
England’s Zak Crawley was named man of the match for his stunning 267 – the 22-year-old’s maiden Test century.
Anderson had been left just one wicket shy of 600 after having four catches dropped off his bowling earlier in the match. One of those at fault was long-time pace partner Stuart Broad, who paid tribute to his teammate on Tuesday.
“He has got better with age and is someone who has inspired me throughout my career, watching him,” he said.
“The last five years in particular, since leaving South Africa in 2016, he’s just gone from strength to strength and he’s a role model to follow for every English cricketer and young cricketer coming through.”