It portrays the US and UK politicians - who are united in their desire for Britain to exit the EU - engaged in a kiss.
The image is reminiscent of the Berlin Wall graffiti artwork of a kiss between ex-Soviet leader Leonid Brezhnev and East Germany’s Erich Honecker.
The mural is in The Carriageworks in Stokes Croft, which is part of a collection of buildings considered to be one of the city’s biggest eyesores. The Stokes Croft area is also known as the spiritual home of artist Banksy.
The text below the graffiti artwork suggests that voters who are against the pro-Brexit transatlantic union should register to vote ahead of the referendum on June 23.
Campaign group We Are Europe has claimed responsibility for the artwork.
“The referendum on June 23 is one of the biggest political decisions of our lifetime and we couldn’t stand by and watch it be dominated by political infighting, negative arguments and middle-aged trolls,” they said.
“This is our future - so we decided to take it back. And this starts by taking back the internet, through a positive campaign that we can all believe in.”
Former London mayor Mr Johnson is leading a campaign for Britain to leave the EU while US presidential hopeful Mr Trump believes the UK will also leave.
The Bristol mural is similar to the picture My God, Help Me to Survive This Deadly Love, sometimes referred to as the Fraternal Kiss, a 1990 graffiti painting on the Berlin wall by Dmitri Vrubel.
It depicts Brezhnev and Honecker in a fraternal embrace, reproducing a photograph that captured the moment in 1979 during the 30th anniversary celebration of the foundation of the German Democratic Republic.