Brand, 51, once one of Britain's most high-profile broadcasters and former husband of US singer Katy Perry, faces three counts of rape, three counts of sexual assault and one count of indecent assault relating to six women from 1999 to 2009.
He denies all the accusations and will set out his defence in court at a later date.
"Today I feel blessed," he said as he arrived with wife Laura Gallacher at London's Southwark Crown Court on Wednesday.
"I feel of course concerned but hopeful that this process will lead to good outcomes for everybody involved."
Opening the case against him, prosecutor Riel Karmy-Jones KC said the six women who had made the allegations had come across Brand either through their jobs, work social events or at gigs in which he was performing.
Some of the women had protested and said no to him while others had no opportunity to react to his advances.
It had made no difference to Brand, she said.
"His desire, his strong desire, for some form of sexual contact was indiscriminate and voracious," the prosecutor said.
"He could be nice when he wanted to be, funny - undoubtedly - charming, likeable even - when he wanted something in return.
"But then demanding, entitled, a flirt with a huge sexual appetite, child-like in his expectation that his every desire should be met. He was ruthless, he was calculating, he was manipulative and, the prosecution say, he was a sexual predator."
Karmy-Jones said the places where the alleged incidents took place included a hotel room, workplaces, a toilet cubicle in a bar and at his home address.
"He cared not who the woman was, what state she was left in or how he had left her feeling," she said.
"Uppermost in his mind was his insatiable desire to get what he wanted with whomever he wanted it with."
The women involved did not know each other and had not taken the matter to the police at the time for various reasons, the prosecutor said.
However, following a TV program and a media report in 2023 in which anonymous allegations were made against Brand by accusers who were not involved in the current trial, they had come forward with their complaints.
Brand sat in the dock wearing a dark suit and thin, white scarf, staring forward intently during the trial, which is expected to last about six weeks.
The comedian, known for his flamboyant style and appearance, was a regular on British television screens in the 2000s and also worked as a radio presenter for the BBC.
He went on to star in a number of films including Get Him to the Greek in 2010, the same year he married Perry.
They divorced in 2012 after 14 months of marriage.
More recently Brand has mainly appeared in online broadcasts, with content often focused on US politics, religion and free speech.
