The Metropolitan Police force said Roman Lavrynovych, who was arrested on Tuesday, was charged with arson with intent to endanger life.
The charges are linked to three incidents over the past week - a car fire on May 8, a fire on Monday at Starmer's private home that damaged the door of the house and a fire on Sunday outside a north London house converted into apartments connected to the leader of the United Kingdom.
No injuries were reported from any of the fires.
Lavrynovych, a Ukrainian citizen, is due to appear in court on Friday.
After he was arrested, Lavrynovych has remained in custody after warrants of further detention were obtained, the police said in a statement.
Starmer moved with his family to the prime minister's official Downing Street residence after taking office in July.
The investigation was led by counterterrorism detectives as it involves the prime minister.
Authorities are also probing whether there was state involvement as well as looking at other potential motivations.
Earlier this week, Starmer said the recent arson attacks represented "an attack on all of us, on democracy and the values that we stand for".
The attacks were condemned by leaders across the House of Commons, including by the Conservative Party's Kemi Badenoch, who described them as "completely unacceptable".
Starmer's former house has attracted protesters in the past.
Last year, three pro-Palestinian activists were arrested and charged with public order offences after unfurling a banner covered in red handprints outside the building.
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