The defender has also vowed to be a competitive and decisive member of the Villa team.
The 21-year-old left back joined the club from French side Nice at the weekend as manager Tim Sherwood looks to strengthen his side ahead of the Premier League season.
He officially joined up with his new club on Monday and says he is desperate to become a fan favourite in the side as the supporters play an important role at every football club.
"I want to make a big bond with the supporters,” he told avfc.co.uk.
“I want them to be proud of me as a football player. I want them to see me and think that he is a good player for the team. It's important because fans mean a lot to every football club.”
Keen to be a competitive and decisive player for Villa
Many Villa fans will be hoping things go slightly better for their side next season, having flirted dangerously with relegation over the last few years.
Tim Sherwood had them playing better football when he arrived in January though, with their run to the FA Cup final and the football they played having increased expectations somewhat.
Unfortunately for him they have already lost key players Ron Vlaar and Fabian Delph this summer, with Christian Benteke likely to join those two.
They were decisive players last season, and Amavi says he is looking to be one as well, while also bringing his competitive nature to the side.
"I want to play well for this football club. I am determined to do that,” he added.
“I want to make rapid progress. I will be a decisive player. I will bring my combative nature to the side. I will fight for them every single match. Hopefully they will enjoy that.”