The Premier League club smashed their transfer record to sign Ozil for 42.5 million pounds on Monday, days after he said he would stay with the nine-times European champions for a fourth season.
Ozil sulked after Ancelotti substituted him in last month's La Liga match at Granada and the Italian then left him on the bench for Sunday's 3-1 victory at home to Athletic Bilbao.
"I was certain...that I would stay at Real Madrid," Ozil said in an interview published on the German federation's website on Tuesday.
"Then I realised that I didn't have the confidence of the coach and the officials after all," added the 24-year-old of Turkish origin.
"I am a player who needs that confidence and I saw that I would have that at Arsenal and that is why I am going there."
Ozil's departure, which followed Real's purchase of winger Gareth Bale from Tottenham Hotspur for a world-record fee of 100 million euros (£85.3m), prompted head-scratching in Spain as he was one of Real's most creative squad members.
He made 31 assists in his last two seasons, the most of any player in La Liga, and had developed a lethal partnership with Real's Portugal forward Cristiano Ronaldo.
Ozil said he was happy to be joining up with Germany team mates Lukas Podolski and Per Mertesacker at Arsenal and the fact that the London club's manager Arsene Wenger spoke German would help him to settle in.
"Wenger gives me the confidence that I can develop further and I want to be in top form for the World Cup next year," he said.
"I spoke to him for a long time on the telephone and he told me his expectations and he trusts me, which I need as a player.
"I am a player who always wants to play a whole match, the full 90 minutes.
"I am looking forward to the new challenge. I have already heard that they (Arsenal) have fantastic fans, the city is great and the team is of a very high quality."
Real fans who gathered at the Bernabeu for Bale's presentation on Monday chanted for Ozil to stay and the player had warm words for the supporters of his former club.
"It makes you sad of course when you hear things like that but I wish my friends there all the best, that they stay healthy and are successful."