The Spain international striker made his switch to the Vicente Calderon Stadium after spending three years with the Spanish champions.
And Villa has explained he was on the verge of signing for Arsene Wenger's side in January, only for Barca to block the deal.
"Arsenal's offer was very good for the club and great for me, but they (Barcelona) did not deem it feasible for me to leave at that time. I was told that I was needed," Villa told Canal+.
Since scoring on his debut in the first leg of the Supercopa de Espana against Barcelona, Villa has amassed eight goals in La Liga during what has been an impressive campaign so far from Diego Simeone's men.
As well as sitting second in the table, Atletico have also qualified for the knockout stage of the UEFA Champions League after topping Group G, with Villa pleased to have joined the club.
"I'm happy (that I joined Atletico) because my goals and performance on the field have helped the team to achieve their goals," he added.
"After all, as you know, I think more (as a) collective than (an) individual.
"The club (Barcelona) has always shown me great affection, and fulfilled their promise to sell me in the summer. I have only words of gratitude for Barca."
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
