Watson went for five times his base price and will join the likes of Virat Kohli, AB de Villiers and Chris Gayle who have been retained by Bangalore.
Watson, who struck an unbeaten 124 against India in a recent T20 game, was bid for aggressively in the opening session, which saw Sunrisers Hyderabad buy allrounder Yuvraj Singh for just over one million dollars and Rising Pune Supergiants take England's Kevin Pietersen for $515,000.
Watson earlier played for Rajasthan Royals, which is suspended for two years along with Chennai Super Kings over contact by officials with illegal bookmakers during the 2013 season.
In a big surprise, uncapped allrounder Pawan Negi emerged as the second most expensive player at the auction at $1.25 million.
The slow left-arm bowler and handy batsman, who is in India's squad for a home T20 series against Sri Lanka next week as well as the Asia Cup and World Twenty20, was bought by Delhi Daredevils.
South African allrounder Chris Morris also went for a high price of just over a million dollars to Delhi, which already has his compatriots Jean-Paul Duminy and Quinton de Kock.
Hyderabad bought pace bowler Ashish Nehra for $810,000 to add to batsmen like Shikhar Dhawan, Australian David Warner and New Zealand's Kane Williamson, and now also Yuvraj.
Dale Steyn of South Africa and West Indian Dwayne Smith were both bought by Gujarat Lions for identical sums of $339,000 while pace bowler Ishant Sharma was taken by Pune for $560,000.
New Zealand batsman Martin Guptill, who has never played in the IPL, was surprisingly not picked by any team despite his superb recent form in limited overs games against Australia, Pakistan and Sri Lanka.
Hashim Amla of South Africa, George Bailey of Australia and Sri Lankan veterans Mahela Jayawardene and Tillekaratne Dilshan were the others not bid for.
A total of 351 players featured in Saturday's auction and the players bought will join those either retained by franchises or players from Chennai and Rajasthan who were picked by new teams Pune and Gujarat in a draft in December.
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