The 23-year-old emerged as a transfer target for a number of European clubs after an impressive couple of seasons for Real Sociedad.
However, it was Atletico that won the race for the Frenchman this summer.
"Why Spain and not elsewhere? This is my championship, my home. I'm happy here and Atletico is a great club. The [champions] were willing to pay €30m (£23.8m) for me," he told France Football.
"I had the boss on the phone. He motivated me and said the club really wanted me. I knew that I was coming here to learn.
"Was it weird when PSG and Arsenal were also interested? [Atletico are] still the champions of Spain! I needed a club like that and a coach like Diego Simeone to progress. I always demands intensity in training. That's my style and I like it."
Griezmann impressed for his country at this summer's World Cup.