The talented Wales youth international, 20, was captain of the Gunners' U23s this season.
"Yes, there were all kinds of reactions, they were in shock, but this is a right move for me and my career. It's my career and I think Dinamo is a step forward," Burton said.
The youngster admits he took inspiration from Dani Olmo, who quit Barcelona's academy for Dinamo two years ago before moving onto RB Leipzig last month.
"Dinamo is a club with a great history and I can't wait to play. I came because Dinamo introduced me to the project and it seemed like a good move, right for my career. It's my first time in Zagreb, but I've been to Croatia before. It's a beautiful country. I didn't know I was the first British player in Dinamo, that's pretty nice.
"Of course Dani Olmo has shown all of us the way to success through Dinamo. I have already played against Croatia U-17 and Dinamo U-19 and there were a lot of Dinamo players. It's nice to be with them now."