The 36-year-old with 564 scalps to his name, is now behind the spin trio of Muttiah Muralitharan (800 terrains) of Sri Lanka, Shane Warne (708) of Australia and Anil Kumble (619) of India on the list of all the times.
Anderson is three years older than starter Alastair Cook, who retired from international cricket after the Oval test.
Anderson, who no longer plays cricket one day for England, believes that he has not finished and wants to achieve more in the longest format of the game.
"I really do not think about it, I think I do my best when I focus on what awaits me, the next game, the next series, whatever."
"I read something that Glenn McGrath said," he added.
"He went to the ashes of 2006 with no intention of retiring and then, in the end, he thought that time was running out, that could happen to me, who knows, I do not like to look too far."
McGrath posted a congratulatory message on Instagram commending Anderson's "dedication, commitment, hard work, dexterity and mental toughness".
And he has challenged the England bowler, who made his debut in 2003 and has played 143 Tests, to continue and reach the 600 mark.
"If he can raise the bar to 600 acres, that's an incredible effort," McGrath told BBC radio.
"Being a fast bowler is the hardest part of the game and injuries play an important role," he added.
"To think that Jimmy played for so long and continued at the top of his game shows his work ethic, his physical and mental strength and everything else that comes into play."
McGrath, who led one of the best teams in the history of the event, said Anderson's record would be maintained for a long time.
"The game is faster, it's faster, and will bowlers play enough Cricket Test in the future to get closer to the brand?"
An emotional Anderson said he would miss Cook's influence in the dressing room.
"For me he has been a very good friend but it has been someone I admire," he said. "His work ethic and the way he behaves himself is a true idol not only for me, but for the rest of the team.
"We'll miss him in that sense, we'll still be good friends in the future, but I'll miss him on tours, in dressing rooms, just that shoulder to lean on when it's not going so well."
(With the entries of AFP)