Kolkata - Australia paceman No buyers for Steyn as Morris fetches staggering R20m at IPL auction
The winning bid in the cash-rich Twenty20 league, beat the previous record $2.16 million paid for England's Ben Stokes in 2007 by the now-defunct Rising Pune Supergiants.
Aussies dominated the bidding war, with all-rounder Glenn Maxwell going to Kings XI Punjab for $1.51 million after recently returning to cricket from a short break due to mental health issues.
The IPL auction is an annual event held before the start of each season where teams buy players who sign central contracts.
The players get around 75 percent of the auction price - effectively their salary for the season - while the rest goes to their national board.
Other big foreign buys included South Africa bowler Chris Morris ($1.4m to Royal Challengers Bangalore), England's World Cup-winning skipper Eoin Morgan ($734 265 to Knight Riders) and Australia limited-overs captain Aaron Finch ($619 303 to Bangalore).
But it was Cummins who initiated the biggest bidding war, with Bangalore and Delhi Capitals upping the ante before Kolkata swooped in to catch their former player, who has claimed 32 wickets in 25 IPL matches.
Cummins said in a video message posted on Kolkata's official Twitter site.
While best for a foreign player, the price paid for Cummins is still short of the 160 million rupees ($2.3 million) that Bangalore paid for Indian batsman Yuvraj Singh in 2015.
Explosive hitter Maxwell made his presence felt as he improved from his base price set at 20 million rupees ($282 000) to re-unite with his former team.
"He has the capacity to really blast through on a good day," Punjab chief executive Satish Menon said after the big buy.
"He is the only guy we see as 'X factor' in the middle-order which we lack very badly. We couldn't have thought anyone better than him. He knows the ground, he Kings XI Punjab the way it has been."
Maxwell has scored 1 397 runs in the IPL at an average of 22.9 at a rapid strike rate of 161.13.
A total of 338 players are under the hammer at the auction for the 13th edition of the cash-rich league.