Brebner, 42, took over at Victory as interim head coach in June, before leading a youthful team to one win and four losses to finish the A-League season.
A two-time championship winner with Victory as a player, Brebner was appointed permanently on Monday.
"I am extremely proud to be appointed the head coach of Melbourne Victory," Brebner said. "The club has been a huge part of my life, and the experience of coaching the team over the past couple of months really fuelled my desire and belief that not only did I want the opportunity to secure the role full-time, but that I had the skills and expertise to do so, and to do it well.
"I have made no secret of the fact that I feel like the club had strayed from its football identity and culture, and I want to help lead the solution.
"Everyone who loves this club wants to see us back playing the Victory way, and I want our members and fans to be proud of how we go about our business.
"It's going to take a lot of hard work but I'm excited about the challenge. The first step will be to build a highly competitive squad."
Victory endured the worst season in its history in 2019-2020, finishing 10th in the table as Marco Kurz, Carlos Salvachua and Brebner were all at the helm.
Anthony Di Pietro, the Victory chairman, was thrilled to welcome Brebner as full-time coach.
"We are delighted to appoint Grant as head coach of Melbourne Victory," he said. "As we said from the outset, we would take the necessary time to find the right person who aligned with both the club's football and cultural philosophy.
"Working through the recruitment process amidst the backdrop of COVID-19 certainly had its challenges, but we are excited to have someone who bleeds blue at the helm, and strongly believe Grant is the right person to lead our A-League program.
"There's plenty of hard work ahead as we prepare for our AFC Champions League campaign and the upcoming 2020-21 A-League season, but it is exciting to finalise Grant's appointment, so we can now look to collectively build our squad and the required support staff, to position our club for success.
"Grant is clear in the style of football Melbourne Victory want to play, and most importantly he has already started building the foundations and culture he believes will help us return to delivering the on-field results expected at our club."