The France left-back agreed a two-year contract with the Serie A champions earlier this month after asking to leave United towards the end of the previous campaign.
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Goal understands Van Gaal was keen for Evra to become a leader in the dressing room after penning a one-year extension in May, but the left-back admitted he had no hesitation in making the switch to Turin once a €2.5 million deal had been agreed.
"It was really difficult to leave Manchester United, it was for personal reasons," he said at a media conference in Turin.
"Three months before the end of the season I asked to speak to other clubs and when I knew Juventus were interested it was an easy decision, but the most difficult thing was to leave Manchester United.
"Manchester had great confidence in me. I spoke to Van Gaal, who was sorry to see me go, but I wanted to come to Juventus."
Juve have won the past three Serie A titles under Antonio Conte but preparations for the new campaign were thrown into doubt when the head coach left his role with the club on July 16.
Massimiliano Allegri replaced Conte at the helm and Evra, who does not have any concerns about the 45-year-old's departure, is ready for the challenges that come with defending the league crown.
"The minute Juventus came calling, I knew it was the right choice for me," he added. "They have the same winning mentality as me.
"Juve wants to win this year, I have never won the championship four times in a row, but it won't be easy. I managed to do it three times with Manchester United and know how difficult the challenge is.
"We hope to do well in the Champions League too. It's a great competition and we'll look to go as far as we can."