England's ecstatic captain Joe Root labelled Anderson's achievements "astounding" and said he hoped he had plenty more Tests ahead of him.
"For him to have taken as many wickets as he has, to even be in the same league as the likes of McGrath, now chasing the big two spinners, is a phenomenal effort and I think the most exciting thing is he's bowling in my opinion probably at his best.
"Throughout this summer he's been outstanding and I can see that carrying forward hopefully for a long time still."
Root described the feats of Cook, who made 147 in the second innings of a 118-run win, and Anderson, as "fairytale stuff".
Root added it was important for England to have won 4-1 after coming into the Oval Test with the series already in the bag, ahead of a three-match contest in Sri Lanka in November.
"I thought everyone played a significant part and role and that's what's been really pleasing for me as captain and hopefully now we can really kick on from this," he said.
"We're going to have different challenges throughout the winter but we know where we want to get to, we know there's a lot of hard work ahead and that we're not the perfect side.
"If we continue with the same attitude and drive and determination then we've got every chance of getting right to the top."