"We are relieved and overwhelmed," May's wife, Diana May, said in the district attorney's office after the verdict was read in court.
The jury took just under six hours to reach a verdict after beginning deliberations Tuesday.
May's family members cried quietly as the court clerk read the verdict early Wednesday afternoon. Jurors found Alvarez guilty of first degree-murder with the special circumstance of killing a peace officer, making him eligible for the death penalty.
Prosecuting attorney Steve Wagstaffe said the verdict was "swift" and reached unusually quickly for a murder trial.
He said that Wednesday morning, the jury, comprised of six men and six women, asked to see 17 pages of transcript from Alvarez's testimony about the shooting, which occurred the afternoon of Jan. 7, 2006.
May had responded to a fight involving Alvarez at the Villa Taqueria in East Palo Alto at about 4:30 p.m. that day. Alvarez and May exchanged gunfire during a confrontation that followed a foot pursuit. Alvarez suffered one bullet wound to the leg, and May died at the scene.
Less than 30 minutes after the jurors received the transcript of Alvarez's testimony, they announced a verdict had been reached, Wagstaffe said.
"The whole issue was, is it murder or self defense?" he said.
Wagstaffe had called the death an "execution," and said that Alvarez shot May twice, then fired two more rounds to "finish him off" after he was on the ground.
Defense attorneys Charles Robinson and Eric Liberman argued that May shot Alvarez first, and that Alvarez fired back out of fear for his life.
The penalty phase of the trial, in which the same jury will decide whether to recommend death for Alvarez, begins Dec. 7 and could last several weeks. At minimum, Alvarez will be sentenced to life in prison without the possibility of parole, Wagstaffe said.