Hook's departure comes as the United Nations Security Council prepares for a vote on a USA push to extend an global arms embargo on Iran.
The promotion comes ahead of a hotly-anticipated UN Security Council vote on extending the arms embargo on Iran.
Hook had been a chief architect of the Trump administration's maximum pressure campaign, which has reimposed economic sanctions on Iran in a bid to bring the Islamic Republic back to the negotiating table after the U.S. unilaterally exited in 2018 a nuclear pact Tehran struck with world powers.
"The Security Council's mission is to ensure global peace and security", said Pompeo. "We need to restore the U.N. Security Council standard of no enrichment", Hook said. It describes Abrams as an "Iran hard-liner"-unlike former secretary of state John Kerry, who injured himself riding a bicycle during negotiations over the terms of USA reparations to the Iranian government".
Abrams, who will now take over both the Iran and Venezuela portfolios, became entangled in the Iran-Contra affair during his tenure in former President Ronald Reagan's administration.
Hook, a longtime Republican foreign policy fixture, was an early arrival in the Trump administration.
As policy planning chief, Hook tried to strengthen the Iran deal, which Trump denounced during the 2016 presidential campaign as the worst deal ever negotiated and pledged to pull out from. Hook praised his own record to the New York Times on Thursday, declaring that "by nearly every metric, the regime and its terrorist proxies are weaker than three and a half years ago".
Trump has scoffed at the USA intelligence findings, notoriously at a joint news conference in 2018 appearing to take President Vladimir Putin's denials of election meddling at face value.
U.S. Special Representative for Iran Brian Hook speaks to VOA Persian at the State Department in Washington, Feb. 26, 2020.
Pompeo has demanded it be unconditionally extended, saying that the UN Security Council is obliged to extend it in the name of security, to prevent Iran from buying whatever weapons it wants.
The departing Mr Hook, he added, "set into motion a range of new strategies that advanced the national security interests of the United States and our allies". Hook twice flew to Zurich, Switzerland, to take custody of freed Americans.