The 28-year-old world record holder equalled the Olympic record - set by Czech Roman Sebrle at Athens 2004 - by scoring 8,993 points in Rio.
France's Kevin Mayer took silver with 8,834, while Canada's Damian Warner secured bronze with 8,666.
"To win two Olympic golds in a row like Daley and Mathias is very special," said Eaton.
"One day, I'm going to have to meet Daley, shake his hand and thank him for giving me something to chase after.
"My throwing has been bad in the past, but I really got after the discus and shot here. Can I do three in a row? Maybe you should ask Daley."
Eaton was the overwhelming favourite to follow Thompson's achievement from 1980 and 84 and is the third multi-eventer, alongside American heptathlete Jackie Joyner-Kersee, to win back-to-back Olympic titles.
He has dominated the event since 2011, claiming back-to-back world titles and twice setting new world records along with his Olympic success.
No British athlete competed in the 10-discipline event.
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Heavy rain in Glasgow has resulted in a waterlogged pitch at Thistle's Firhill Stadium.
Not date has yet been set for the rearranged fixture.
Thistle, who have won their last four games, also had a top-flight match against Motherwell called off due to rain on 5 December.
American Ashton Eaton has become the third man to retain the Olympic decathlon title, winning in Rio to emulate Great Britain's Daley Thompson, and the USA's Bob Mathias.
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The Scottish Premiership game between Partick Thistle and St Johnstone has been postponed following a morning pitch inspection.