DNA evidence recovered from James' body was matched to the defendant, the statement says.
"This defendant is an alleged serial killer who murdered three of his elderly neighbors who trusted him and welcomed him into their homes only to have that trust violated in the worst way imaginable," Gonzalez says in the statement.
"We will do everything we can to seek justice for the victims and the many family members and friends who were left without their loved ones."
Gavin was arraigned on Tuesday and pleaded not guilty.
He was ordered held without bail and will remain in custody until his next court date, which is scheduled for July 6.