Villa told NYCFC.com: "Three years ago, we started a very good project to build this amazing club and they chose me to be the first captain which I'm still so proud of.
"When I look back to those first days in 2014, it's really amazing to see how far we've come in such a short space of time and to know that there is so much potential for us to continue growing, on and off the field.
"I'm so happy here in this city and at this club, I am fit and I can do things on the pitch - I'm not ready to go to the sidelines.
"That's why continuing here and signing this contract was a really easy decision for me."
Villa continued with a message for the fans who've backed him since the day he first arrived in 2015.
"I want to say thank you to everybody for the support – from the first day until now, they love me and I love them. They give me all the support inside and outside of the pitch and they are a huge part of our successes, both in the past and the ones to come in our future."
His Head Coach Patrick Vieira also expressed his pleasure that his frontline marksmen has committed his future.
Vieira said: "It's really good news for me, it's good news for the club and it's good news for David, especially when you look at the way he's been playing and the amount of goals he's scored.
"The club wanted to give him another year and he wanted to stay for another year. All of the parties are really happy and I'm personally really pleased that he will be with us for that time."