Tymal Mills went for £1.4m to Royal Challengers Bangalore, while fellow England bowler Chris Woakes was bought by Kolkata Knight Riders for £504,140.
England one-day captain Eoin Morgan has gone to Kings XI Punjab for £240,066.
International team-mates Jason Roy and Chris Jordan were sold to Gujarat Lions and Sunrisers Hyderabad respectively.
Batsman Roy, 26, fetched £120,000, while 28-year-old fast bowler Jordan cost £60,000.
Stokes, 25, had a base price of £240,000 (20 million rupees) but was the subject of bids from Mumbai Indians, Royal Challengers Bangalore, Delhi Daredevils and Sunrisers Hyderabad before Pune emerged successful.
His fee overtakes that of former England duo Kevin Pietersen and Andrew Flintoff, who were sold for $1.55m (£1.1m) each in 2009.
Stokes, Roy, 24-year-old Mills and Woakes, 27, will be playing in the eight-team Twenty20 competition - which takes place between 5 April and 21 May - for the first time.
"It's a life-changing amount of money," said Stokes. "Seven times my base amount - that's mental but pretty cool to think about.
"It was hard to follow on Twitter. I wasn't sure how much a Crore [Indian unit of measurement] was - people were retweeting stuff, and it was complete carnage.
"I'm just seriously excited about getting going."
Jos Buttler was retained by Mumbai Indians and Sam Billings was kept on by Delhi Daredevils during the first round of 2017 IPL auction held in Bangalore, but batsmen Alex Hales and Jonny Bairstow went unsold.
"Great day for English cricket and a few lads in particular. Congrats boys," said Buttler.
Left-arm pace bowler Mills will be available for the whole tournament as he is limited to playing T20 cricket because of back pain.
"When it finished I did not know how much it was worth," he said. "When I worked it out I could not believe it - it did not seem real.
"It's an amount of money that can change your life. It will for me."
England's other players may not be available for the 10th edition of the competition because of international commitments as England host Ireland in one-day matches on 5 and 7 May.
They then host South Africa in a three-match ODI series, with the games scheduled to take place on 24, 27 and 29 May, before the ICC Champions Trophy starts in England on 1 June.
Pune owner Sanjiv Goenka said Stokes was a "complete player".
We've been lacking this one genre of player," he said. "We have many heroes but this is the one hero that we were lacking.
"We knew he was going to be expensive. We do believe he is going to be there for the first 14 games."
Stokes helped England reach the final of the World Twenty20 in 2016, but they were beaten by the West Indies after the all-rounder was hit for four consecutive sixes in the final over by Carlos Brathwaite.
The Durham player was also part of England's winter tour of India and were beaten 4-0 in the Tests series, 2-1 in the ODIs and 2-1 in the T20 series.
He has become one of England's best performers and was named vice-captain of England's Test team after Joe Root took over as skipper from Alastair Cook earlier this month.
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Mills is England's fastest bowler but has played only four T20 games at international level.
"We really needed bowlers, especially with Mitchell Starc not being available for this edition and, therefore, Tymal Mills was a great buy," said RCB chairman Amrit Thomas.
"He suits the playing conditions in Bangalore and we would have done absolutely whatever was required to get him."
In other notable highlights from the auction, all-rounder Mohammad Nabi became the first Afghanistan player to be bought in the IPL, with Sunrisers Hyderabad picking him up for £36,000.
England all-rounder Ben Stokes became the Indian Premier League's most expensive foreign player when Rising Pune Supergiants bought him for £1.7m.