The teams met in the third/fourth playoff of the final leg of the World Series in Amsterdam, with England -- who will represent Britain -- scraping it 15-14.
The result put them level with the U.S. on points but above the States in the all-important series fourth place on points difference.
Canada won their first tournament when they beat Australia 20-17 in the final, but both teams had already earned their Rio slots on Friday, along with New Zealand.
The Kiwis were the first to secure a berth last week and were crowned World Series champions for the third year in a row on Saturday.
Rugby sevens, for men and women, is appearing in the Olympics for the first time next year.
(Writing by Mitch Phillips in London, editing by Douglas Beattie)
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