The 36-year-old downplayed his personal achievement, saying he was more focused on helping England win the final match of the series.
England wrapped up victory at the Oval on Tuesday, winning the final match of the series against the number one side in the world by 118 runs
Root described the feats of Cook, who made 147 in the second innings of a 118-run win, and Anderson, as "fairytale stuff".
Anderson, who now has 564 scalps, said he was happy his friend was on the field to witness his record.
India were dismissed for 345 on the fifth and final day, having been set a mammoth 464 for victory.
James Anderson removed Mohammad Shami to go past McGrath's tally of 563 wickets
The former England captain, about to become a father for the third time, said it was difficult to put his achievement into words
Cook made 147 and Joe Root, his successor as England captain, 125 as the hosts piled up 423 for eight declared in their second innings
The 33-year-old opener reached the landmark in unusual fashion when an overthrow from Jasprit Bumrah that went to the boundary
South Africa name depleted squad for Pakistan T20Is owing to IPL constraints
PCB decides to resume PSL 2021 in June
'It was a joint decision' - Silverwood on Archer's omission from ODI side
Bravo century, Pollard blitz lift West Indies to series whitewash over Sri Lanka
PSL 2019 - PSL Schedule with all PSL 4 Matches and Schedule for all Franchises
MS Dhoni has never scored a century outside Asia
PCB announces major salary hike for domestic cricketers in new pay structure
Sarfraz Ahmed captaincy record
PSL Schedule Live Streaming and PSL 5 Matches Details
Amad, Akmal power Balochistan to comprehensive win over Sindh