The lawsuit is over an opinion piece Ms Heard wrote for the Washington Post in which she called herself a victim of domestic violence. He denies any abuse.
Ms Heard has sued back, with a $100m counterclaim against Mr Depp.
The closely watched civil trial, which is taking place in Virginia, is now in its second week.
Ms Heard's team has portrayed Mr Depp as an abusive partner prone to drug and alcohol binges.
Mr Depp's team has presented Ms Heard's claims of domestic violence as a "hoax" and a calculated strategy to ruin his reputation.
Speaking to the jury on Tuesday, Mr Depp said the truth was all that mattered to him now.
"I never struck Ms Heard in that way, nor have I struck any woman in my life," he testified, adding that "her accusations sort of permeated the industry".
"It's been six years of trying times - so strange when one day you're Cinderella, so to speak, and then in 0.6 seconds, you're Quasimodo," he said, describing how people's attitudes towards him changed after Ms Heard's op-ed was published.
The trial has focused so far on Mr Depp's demeanour and whether he was ever verbally or physically abusive towards Ms Heard. Lawyers for Mr Depp have accused his ex-wife, an actress, of giving the "performance of her life" in her descriptions of alleged abuse.
Mr Depp began his testimony saying that Ms Heard's claims are "not based in any species of the truth".
His lawyer went on to ask him to describe his childhood in Kentucky, and the abuse that he suffered from his mother.
"I could see when she [his mother] was about to head into a situation where she was going to get riled up and someone was going to get it. And generally it was me," he said.
Ms Heard is also expected to testify later in the trial.
The jury has heard evidence presented by the celebrity ex-couple's former therapist, who described how Mr Depp and Ms Heard engaged in "mutual abuse", as well as from medical workers who treated Mr Depp as he was detoxing himself from opiates.
On Monday, a nurse who was hired to treat Mr Depp's drug addiction and attended the couple's wedding testified that she witnessed Ms Heard "try to instigate" conflict with her former husband on several occasions.
She would sometimes pick fights with him while he was receiving medical treatment, said nurse Debbie Lloyd, who frequently travelled with Mr Depp.
On Tuesday, a sound engineer who has worked with Mr Depp on nearly all of his movies since the 1990s testified to having never witnessed the actor verbally or physically abuse his two children or their mother.
Keenan Wyatt, who is also a friend of Mr Depp, described how the actor wears an earpiece during filming to listen to music and occasionally have lines fed to him.
The trial is expected to last at least six weeks.
Ahead of the case, Ms Heard wrote on social media that she never identified Mr Depp by name in her 2018 op-ed.
"Rather, I wrote about the price women pay for speaking against men in power," she said.
"I continue to pay that price, but hopefully when this case concludes, I can move on and so can Johnny".