The White House said it was "the toughest sanctions regime ever imposed on Iran" and targeted Iran's energy, shipping and banking sectors.
However, eight countries will not be penalised by the US for continuing to import Iranian oil.
President Donald Trump withdrew from the deal in May, describing it as "defective at its core".
"Sanctions are coming," he tweeted after Friday's announcement, referencing the TV series Game of Thrones and its motto "Winter is coming".
The US has been gradually re-imposing sanctions since it unilaterally withdrew from the agreement, but analysts say this move is the most important because it targets the core sectors of Iran's economy.
An Iranian foreign ministry spokesman said Iran was unconcerned at the return of sanctions, Reuters reports.
The agreement saw Iran limit its controversial nuclear activities in exchange for sanctions relief.
Barack Obama, the US president at the time, had argued the deal would prevent Iran from developing nuclear arms.
The UK, France, Germany, Russia and China were also parties to the 2015 accord and have stuck to it, saying they will set up a new payment system to maintain business with Iran and bypass US sanctions.
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