Broad and Anderson surpassed McGrath and Warne's combined wickets tally in Test cricket.
McGrath and Warne had a combined total of 1001 wickets in Tests and the pair of Broad and Anderson has now 1005 scalps to their name.
They achieved the feat after Broad ran through the New Zealand batting line-up on Day 3 of the opening Test in Mount Maunganui.
The lanky fast bowler claimed four wickets in the second innings to reduce the Kiwis to 63/5 in the chase of 394.
Speaking after the day's play, Broad expressed his delight in going past two of his childhood heroes – McGrath and Warne.
"New Zealand is a special country for us," Broad told BT Sport. "Back in 2008 at Wellington, we came into the team together and to go past two heroes of mine growing up - McGrath and Warne - certainly we're not in the category or quality of those two.
"They were absolutely heroic in what they did for the game."
"But just to be up there with those two and to have taken the amount of wickets as I have with Jimmy."
Hailing Anderson, Stuart Broad said he was lucky to be born in the same era as the former.
"I feel very lucky to have been born in the same era as Jimmy because without him, I wouldn't have been able to be at the other end taking wickets in the partnership that we've had.
"I've learnt so much from him throughout my career and he's probably the reason I'm still going at 36. He's a great leader to follow," Broad stated.