The Anderson-Tendulkar Trophy will be awarded in all future Test series between the two sides, replacing the Pataudi Trophy in England and the Anthony De Mello Trophy in India. The next five-Test series begins at Headingley on Friday.
The newly designed trophy features the engraved signatures and action images of the two most-capped players in Test cricket.
India batting great Tendulkar played 200 matches and scored 15,921 runs, the most in the format.
England's Anderson, who announced his retirement earlier this year, took 704 wickets in 188 Tests, the most by a fast bowler. The seamer ranks third on the all-time list, behind only spinners Muttiah Muralitharan and Shane Warne.
"For me, Test cricket embodies life... It is the highest form of the game that teaches you endurance, discipline and adaptability, against all odds," Tendulkar said.
"India and England have played a big role in shaping Test cricket in a way that it remains an evolving inspiration for subsequent generations.
"And now, as I share this recognition with my on-field challenger and an off-field gentleman James, I hope that the world celebrates the essence of Test cricket even more - allowing it to traverse boundaries yet untrodden."
Anderson added: "The rivalry between our two nations has always been something special, full of history, intensity and unforgettable moments.
"To be recognised in this way is a real honour. I'm looking forward to seeing the next chapter unfold in England this summer."
The Pataudi Trophy, introduced in 2007, was named in honour of Iftikhar Ali Khan Pataudi, the only cricketer to play Tests for both India and England, and his son Mansur Ali Khan Pataudi, former India captain.
The ECB said the Pataudi family will continue to be honoured, with a new Pataudi Medal to be presented to the winning captain after each series.
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