The Spanish playmaker, a serial winner with Real Madrid and PSG, joined Villa on loan in January for a fresh challenge.
Asensio has already made his mark, scoring twice in the second half to complete a stunning 2-1 comeback win over Chelsea.
"I wanted to try to experience life outside Spain," he told Sky Sports.
“I have already won everything at club level with Real Madrid. In Paris, I also had the opportunity to win titles. This is a new goal, an ambitious project with a coach who wants to win.
"He has that mentality and the players have it too so I am really looking forward to what is left of this season because I believe there are lots of important challenges ahead for Aston Villa and we can feel that the support of the fans is there to help us achieve it.
"It is incredible how they support us and encourage us. If you put that all together, the club, coach, players and fans, we believe that we can aspire towards achieving the maximum this year in the Premier League, the Champions League and the FA Cup."