South Africa all-rounder Chris Morris fetched a record £1.6m bid by Rajasthan Royals.
Moeen, who has departed the England squad in India following the second Test to take up a pre-determined period of rest, found himself at the centre of a battle between Punjab and Chennai for his services.
The 33-year-old, who had spent the past two years with Royal Challengers Bangalore, fills the Super Kings’ final overseas spot and will line up alongside England team-mate Sam Curran at the IPL franchise, when the competition takes place from April to June.
Malan, currently ranked top in the world Twenty20 rankings, is set to play for Punjab following a successful bid of almost £150,000.
And in landing Malan, Punjab head coach Anil Kumble, believes he could have picked up the biggest bargain in the auction.
“Dawid Malan is a very, very good buy,” said Kumble.
“He’s the No 1 T20 batsman in the world, so it is good to have one of the best around joining our squad,”
However, England players Alex Hales, Jason Roy, Sam Billings and Yorkshire spinner Adil Rashid all went unsold during the first round of the auction.
Australian Steve Smith, not retained by the Rajasthan Royals, was sold to Delhi Capitals for £220,000, while batsman Glenn Maxwell will join Royal Challengers Bangalore for £1.4m.
Eight English players – including white-ball captain Eoin Morgan, Ben Stokes, Jofra Archer, Jos Buttler and Jonny Bairstow – were retained by their respective franchises ahead of the 2021 tournament.
Bowler Mark Wood, however, had requested to be withdrawn from consideration for the auction as he did not want to spend more time away from his family.
Reflecting on the auction, Bairstow said: “The qualities Mo has are worth every penny and it really is fantastic to see him go for that amount.
“You can’t necessarily compare individuals, it goes on the balance of what teams are looking for. Riley Meredith, Jhye Richardson, Kyle Jamieson have all fetched over one million US dollars (£716,000).
“If they want to fill a certain role, they will be going for you no matter what.”
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