On Tuesday, Trump announced the decision to withdraw from the Iran nuclear deal, also known as the Joint Comprehensive Plan of Action (JCPOA), which agreed to lift crippling economic sanctions on Iran in return for its agreement to limit its sensitive nuclear activities and allow international inspectors access to its facilities.
Speaking at the House of the Commons, Johnson said: "The JCPOA is an international agreement painstakingly negotiated over 13 years under both Republican and Democratic institutions and enshrined in UN resolution 2231."
"Britain has no intention of walking away," he said.
The JCPOA is an international agreement reached in Vienna in 2015 between Iran, the P5+1 (the five permanent members of the UN Security Council -- China, France, Russia, United Kingdom, United States -- plus Germany), and the European Union.
"Instead, we will cooperate with the other parties to ensure that while Iran continues to restrict its nuclear program then its people will benefit from sanctions relief in accordance with the central bargain of the deal," he said.
Britain would remain "a party" to the JCPOA as long as Iran complied with it, he added.
Britain, France and Germany on Tuesday pledged to remain in the nuclear deal despite Trump's decision to pull US out of the agreement.
In a joint statement, the countries expressed "regret and concern" over the decision and urged Iran to "show restraint" in its response.
Meanwhile, Iranian President Hassan Rouhani said that his country would remain in the deal as discussions with allies take place over the next "few weeks."