The jury returned the guilty verdict by a majority of 10 to two.
Brandt wept and held his hands over his face after the verdicts were returned.
Explaining why he wanted to meet Dame Penny, the former elected member of East Hampshire District Council said he wanted to commiserate with her over her leadership bid.
He added: “I wanted to congratulate her because she was a reforming leader of the Commons, I wanted to congratulate her on the coronation, chat to her about her time in office, have her sign a copy of her book.
“It was entirely political and entirely harmless.”
Clearly emotional at times, Dame Penny told the court: “The difference between this case and even threats to shoot me and my family [is that] they are easier to deal with because that threat is not constantly present.
“It’s not something you are having to think about every single day when you are leaving your house.
“I believe this man was a real threat to me and still is.”
Brandt was released on conditional bail ahead of sentencing on 16 January.
