Having become the first England bowler, and just the sixth in history, to reach the landmark figure on Friday, the 35-year-old Anderson carried on to post new Test-best figures of seven for 42 on Saturday as West Indies were dismissed for 177 in their second innings.
That left England with a target of just 107 for a 2-1 series victory and they duly knocked off the runs in 28 overs to win with more than two days to spare.
"Playing a Test match here at Lord's is always special, but this week will live with me for a long time," Anderson told Sky Sports.
"My family have been here, my friends have been here, and to share the moment with guys I've played over 100 Tests with as well is extra special," the Lancashire paceman added.
Anderson, who made his Test debut at Lord's back in 2003, needed just four balls Saturday to take his third wicket of the innings after a double strike on Friday.
He then claimed two in three balls after lunch, including the key wicket of Shai Hope for 62 as West Indies' man-of-the-series was caught behind off an excellent leg-cutter.
That double success started a collapse that saw West Indies lose their last four wickets for just 22 runs.
"Jimmy's performance speaks for itself," said England captain Joe Root. "To be able to hold a length and put guys under pressure is a great skill.
"He's a massive part of our dressing room and I'm sure he will be for a long time to come."
Once Anderson had bowled Kemar Roach to wrap up West Indies' second innings, it was just a question of what margin England would win by and how quickly they would do it.
Cook's exit, lbw for 17 to leg-spinner Devendra Bishoo's first ball of the innings, denied England a 10-wicket success.
But under pressure top-order batsmen Mark Stoneman (40 not out) and Tom Westley (44 not out) saw England to their meagre target without further loss.
Victory meant Root has won both his first two Test series as England captain after a 3-1 success against South Africa earlier in the season.
"I'm very pleased," Yorkshire batsman Root told BBC Radio's Test Match Special after what was England's last match at this level match before they begin their Ashes defence against Australia in Brisbane in November.
"In the second innings Jimmy was outstanding.
"The ball looked out of shape, I don't know how he managed to get seven wickets with it."
For West Indies, the huge consolation of the series was the way they bounced back from an innings defeat in the opener at Edgbaston to draw level days later with a five-wicket win in the second Test at Headingley.
That was just their fourth away victory, excluding matches against Bangladesh and Zimbabwe, in 88 Tests.
It was built on two hundreds from Hope, his first in Test cricket, and the 23-year-old Barbados batsman appeared to have come of age during this series.
"In the second innings we didn't bat as well as we would have liked," said West Indies captain Jason Holder.
"But Shai Hope batted extremely well and we have a lot of positives to take," added the all-rounder.
"Credit must go to James Anderson. He is a world-class bowler and I'd like to congratulate him on 500 wickets, but I want to urge our guys to keep going."
Ben StokesEngland vs West IndiesEngland vs West Indies 2017James AndersonJason HolderJoe RootKraigg Brathwaiteshai hope
First Published: September 10, 2017, 10:34 AM IST