Brand, 51, the former husband of US singer Katy Perry, is on trial facing 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 at London's Southwark Crown Court.
"I feel of course concerned but hopeful that this process will lead to good outcomes for everybody involved."
Prosecutor Riel Karmy-Jones said some of the six women had protested 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," she said.
Although he could be funny and charming when he wanted something, he also had a childlike expectation his every desire should be met, she added.
"He was ruthless, he was calculating, he was manipulative and, the prosecution say, he was a sexual predator," Karmy-Jones said.
The alleged offences took place over a decade as Brand progressed from gigs as a stand-up comedian to a TV presenter, actor and Hollywood movie star.
The first is alleged to have occurred in 1999 when he was performing in a show on the fringe of the Labour party conference in Bournemouth.
The first complainant, who had watched the show and had assumed Brand was gay, said he had raped her in her hotel room where she had invited him to talk.
Mark Pinheiro, one of his co-performers at the show who Brand went on to live with for about a year, said Brand bragged that he had wanted to bed 5000 women in his lifetime.
Giving evidence, Pinheiro said on their last morning in Bournemouth, Brand had returned to where they were staying looking flustered and told them they had to immediately leave.
Pinheiro said that, a couple of months later, Brand admitted he had met a woman the night before and things "may have gone a little bit too far".
Brand's lawyer Ian Winter suggested to Pinheiro that he did not mention that when he first contacted police and no such conversation took place, which Pinheiro rejected.
The second charge relates to 2001, when he is accused of trying to drag a woman into a toilet cubicle at MTV Europe where she worked.
Three years later, a woman said he had dragged her into a toilet cubicle in a bar before orally raping her.
Around the same time in 2004 or 2005, a woman working at a media company said he indecently assaulted her.
The fifth complainant, a fan, had consensual sex at his home in 2009 but then he anally raped her, the prosecutor said.
The sixth, who worked for Channel 4, alleges Brand had demanded a massage and then pressed his face into her groin, also in 2009.
When interviewed by police, Brand declined to answer questions but provided written statements in which he said he did not remember the incidents and had never engaged in non-consensual activity, Karmy-Jones said.
The women involved did not know each other and did not contact the police until after a TV program and a press report in 2023 in which anonymous allegations were made by other women, the prosecutor said.
Brand sat in the dock wearing a dark suit and thin white scarf, staring forward intently.
His trial, expected to last about six weeks, has attracted huge media attention.
The comedian, known for his flamboyant style and appearance, became famous in the UK before starring in a number of films including Get Him to the Greek in 2010, the same year he married Perry.
They divorced in 2012.
More recently Brand has appeared in online broadcasts discussing US politics, religion and free speech.
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