Hibernian led 2-0 after the first leg but goals by Jason Scotland and Anthony Abreu 10 seconds from the end of stoppage time sent the game into extra time with the teams locked at 2-2.
Neither side could find the net in the extra 30 minutes and Hamilton goalkeeper Kevin Cuthbert saved two spot-kicks in the shootout to give his side a 4-3 win on penalties.
Hibernian, four-times Scottish champions, will join Edinburgh rivals Heart of Midlothian, relegated after being deducted 15 points due to financial problems, and 54-times Scottish champions Rangers in the first division next season.
Rangers were relegated to the fourth tier of Scottish football in 2012 after going into liquidation but have been promoted the last two seasons to get back into the (second tier) first division.
Hamilton return to the top flight after a three-year absence. They finished second in championship behind Dundee who were promoted automatically.
(Reporting by Ed Osmond, editing by Rex Gowar)
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