Supporters said they were planning to stage songs, speeches and readings in several European cities.
Assange, 44, is wanted for questioning over a 2010 rape allegation in Sweden but has been inside Ecuador's UK mission for four full years in a bid to avoid extradition.
The anti-secrecy campaigner, who denies the allegation, walked into the embassy of his own free will on June 18, 2012, with Britain on the brink of sending him to Stockholm, and has not left since.
His lawyers say he is angry that Swedish prosecutors are still maintaining the European arrest warrant against him.
The Australian former computer hacker fears that from Sweden he could be extradited to the United States over WikiLeaks' release of 500,000 secret military files, where he could face a long prison sentence.
Listed participants in Sunday's anniversary events include Patti Smith, Brian Eno, PJ Harvey, Noam Chomsky, Yanis Varoufakis, Ai Weiwei, Vivienne Westwood, Michael Moore and Ken Loach.
Croatian philosopher Srecko Horvat, an event organiser, said: “We live in a critical time. We are gathering all around the world on June 19 to speak out for Julian, because he has spoken out for all of us.”
Veteran leftist film-maker Loach said Britain's legal system was “being manipulated to keep a brave man in isolation” and that “all who care about freedom of information should demand that the threats made against Julian should be lifted.
“He should be able to leave his place of safety without fear of deportation or being handed over to those who intend him harm.”
A hero to supporters and a dangerous egocentric to detractors, Assange founded WikiLeaks in 2006 and has been portrayed in two movies in recent years.
Assange has compared living inside the embassy — which has no garden but is in the plush Knightsbridge district, near Harrods department store — to life on a space station.
His 15 feet by 13 feet (4.6 by 4 metre) room is divided into an office and a living area. He has a treadmill, shower, microwave and sun lamp and spends most of his day at his computer.
He got a cat in May to give him some company.
Last month a Stockholm district court maintained a European arrest warrant against Assange, rejecting his lawyers' request to have it lifted.
“The court considers that Julian Assange is still suspected of rape… and that there is still a risk that he will abscond or evade justice,” it said in a statement.
Assange will appeal the ruling, one of his Swedish lawyers, Per Samuelsson, told AFP.
“He is not surprised but very critical and angry,” he said.
Assange's lawyers requested the lifting of the warrant after the UN Working Group on Arbitrary Detention issued a non-binding legal opinion on February 5 saying his confinement in the Ecuadoran embassy amounted to arbitrary detention by Sweden and Britain.
London and Stockholm have angrily disputed the group's findings.
The alleged crime dates back to 2010 and the statute of limitations expires in 2020.
Assange is calling for Britain to leave the European Union in Thursday's referendum on its membership of the bloc.
He alleges that British authorities “repeatedly use the EU as political cover for its own decision-making”, highlighting the European arrest warrant.