Defoe is in top form with six goals in his last 10 games for club and country.
Villas-Boas said: "I think he has received his confidence from me and he is showing his quality.
"In the summer, we told him we really wanted him here - that is why we spoke with his agent and the chairman about his contract renewal.
"So at the moment, we are extremely happy with what he is doing. And I am sure that is having an impact on the way he feels about himself."