These penalties largely cut Iran out of the worldwide financial system, until they were suspended by Obama under the nuclear deal.
Britain, France and Germany had called on Trump on Thursday to uphold the pact.
While Trump approved the waiver, new, targeted sanctions were announced against 14 entities, including Sadeq Amoli Larijani, the head of Iran's judiciary.
Trump said on Friday he would waive nuclear sanctions against Iran for the last time to give Washington and its European allies a chance to fix the "terrible flaws" of the 2015 nuclear deal.
Trump's Friday announcement will "reflect frustration at European allies and at Congress" for dragging their feet over proposed legislative changes that would call for stricter enforcement of the Joint Comprehensive Plan of Action (JCPOA), Bloomberg News foreign policy reporter in Washington. All sides agreed that it would cover only Iran's apparent efforts to develop nuclear weapons, which was in violation of United Nations resolutions, and not other issues.
Trump stopped short for a third time of re-imposing harsh sanctions meant to push Tehran to give up its nuclear weapons research.
While there may be some relief that Trump has yet to torpedo the hard-won accord, there were clear signs of frustration from European capitals in the runup to the decision.
Most U.S. trade with and investment in Iran already is banned under separate U.S. sanctions for Tehran's human rights abuses, ballistic missile program and support for terrorism, but the administration and its supporters said more are needed.
"And if at any time I judge that such an agreement is not within reach, I will withdraw from the deal immediately".
Washington policy hawks hailed Trump's decision, which they said would concentrate minds in Europe, where leaders have urged the USA president not to sabotage a deal they see as a landmark diplomatic success. It said the sanctions are against global law and go against USA commitments, saying they would bring a "strong reaction" from Iran.
But Trump argues that his predecessor Barack Obama gave away too much to Iran in sanctions relief, without forcing the Islamic republic to end its ballistic missile program and support for militant groups.