The Foreign Secretary went on to say that he wished he could use Twitter to engage people in the same way the President has.
Mr Johnson complimented Mr Trump’s use of social media despite the US leader having recently used it to suggest a female TV presenter was “bleeding badly from a face-lift” and to falsely accuse Barack Obama of bugging his phone.
Mr Johnson is set to accompany Theresa May to the G20, where the Prime Minister will have a one-on-one meeting with Mr Trump.
Speaking to BBC Radio 4’s Today programme, Mr Johnson said: “I think actually that Donald Trump’s approach to politics has been something that has gripped the imagination of people around the world.
“He’s engaged people in politics in a way in which we haven’t seen in a long time with his tweets and all the rest of it.
“I certainly wouldn’t be allowed to tweet in the way that he has, much as I might like to.”
Mr Trump has cast all convention aside in his use of social media, using it to attack jounalists and political rivals and announce foreign policy positions – on one occasion suggesting the UK should appoint Nigel Farage as its ambassador.
More recently he launched an attack on MSNBC TV presenter Mika Brzezinski whom he accused of ‘bleeding badly from a face-lift’.
The broadside led to surging ratings for morning TV show hosted by Ms Brzezinski, whom he referred to as "crazy Mika".
Mr Trump has also used his Twitter account to accuse Mr Obama of wire-tapping his phones, calling the ex-president “bad (or sick)”.
Ms May and Mr Trump are expected to use a bi-lateral at the G20 in Hamburg this weekend to discuss the situation in North Korea, whose government has just successfully tested an intercontinental ballistic missile.
The Prime Minister will also raise the Paris climate agreement with Mr Trump, who believes the treaty should be renegotiated to make it more favourable to the US.
Ms May was pictured holding hands with the President when she visited him in Washington DC earlier this year, a trip on which she handed Mr Trump an invitation to the UK for a state visit.
The trip has since been in doubt, with reports that Mr Trump did not want to come if it sparked mass demonstrations by opponents in Britain.
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