United States ambassador Woody Johnson brushed off Trump's criticism of the building, telling reporters: "The embassy actually is going to really work". America's top diplomat then met some of the marines who are stationed at the embassy.
The new building is slightly outside central London in an area south of the River Thames which is being regenerated, unlike its predecessor, which was in a plush quarter in the heart of the British capital.
Known as the Joint Comprehensive Plan of Action (JCPOA), the deal was forged in 2015 between Iran and the USA, the UK, France, China, Russia, and Germany in a landmark bid to prevent Iran from developing nuclear weapons.
Actually, President George W. Bush's administration made a decision to build a new embassy in 2006 and chose the location in 2008, according to the State Department and the U.S. Embassy.
Mr Tillerson also visited the relocated U.S. embassy.
Asked when there would be a ribbon cutting ceremony, Johnson said: "At some point we're going to do it, but there's no urgency to that". It is absolutely right that we should welcome him here, and it is time for Labour to end their Spartist agitations.
In London, Tillerson is set to meet with British Foreign Secretary Boris Johnson and national security adviser Mark Sedwill to discuss cooperation on Iran, Syria, Libya, North Korea, and Ukraine.
Prime Minister Theresa May is expected to express support for the Iran nuclear deal that the White House now opposes during an informal meeting later today. "We'll do it when the time is right".
Don't dream it's over: EU's message to Britain
It may feel like we've gone too far to turn back, but the European Commission president has said he would be "happy" for us to rejoin the EU after Brexit .
"Sometimes we forget about the importance of our own relationship", he said. 'I mean, we still have the special relationship with the British people.
Tillerson said he is asking that both sides show restraint and minimize civilian casualties, and that the U.S.is aiming to "see what we can do to work together to address turkey's legitimate security concerns".
Meanwhile Tillerson said he "treasures" his relationship with Boris Johnson and insisted the USA and United Kingdom would always have a "special relationship", as he visited the foreign secretary's official residence in London after a meeting with prime minister Theresa May.
"We will also have the opportunity of underlining our firmness on Iran's compliance with United Nations Resolution 2231, which limits access to ballistic capacity and which Iran does not respect", Le Drian said Monday in Brussels ahead of the meeting with his European Union counterparts.
"They discussed the continuing depth and breadth of the special relationship", the statement by May's spokesperson said.
'They agreed on the importance of the worldwide community coming together to counter Iran's destabilising regional activity, and the Prime Minister reiterated the UK's commitment to the Iran nuclear deal'.
A senior USA official said Tillerson's intent is "to close the gaps" in the accord that gave Iran billions in sanctions relief in return for curbs on its nuclear program and to explore more ways to counter Iranian behavior in Syria, Lebanon, and Yemen.
The three countries have agreed to establish a working group which will meet somewhere in Europe during which Tillerson said he "will see what progress we can make". Iranian Foreign Minister Mohammad Javad Zarif said in response that the deal could not be renegotiated.