The Tottenham manager says the Germany international is an undoubted talent but feels his side, and Manchester City, did the best business during the transfer window
The Germany international signed for the Gunners on deadline day in a £40 million deal, smashing the north London side's previous transfer record of £15m in the process.
Ozil is expected to make his debut for Arsene Wenger’s side on Saturday at the Stadium of Light against Sunderland and Villas-Boas says there is no question he is a talented player.
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"It's a €50m transfer for a No.10 that nobody has any doubt over his ability.
"They have lots of players for that position also but they have become even stronger with Ozil. The fact that Real Madrid sold him to Arsenal for that price, we can't say anything – we are happy with what we have and Real Madrid are happy.
"We are happy with what we have done in the transfer window, extremely happy. Arsenal did a great last-minute coup with Ozil but they will be as competitive as they were before."
Villas-Boas enjoyed a busy transfer window, breaking the club's transfer record three times with the signings of Paulinho, Roberto Soldado and Erik Lamela.
And the Spurs boss feels his side, along with Manchester City, were the biggest winners during the summer, despite losing Gareth Bale to Real Madrid.
"All of us have did good business in the transfer window - Manchester City and us maybe a little bit more than Manchester United, Chelsea, Arsenal and Liverpool," he added.
"I think all of us have made big steps forward from the season before.
"We have done lots of activity in the transfer market. We have been involved with a couple of transfers that we couldn't get through for various reasons and we are extremely happy with what we have done.
“We have lost a couple of players – players who were also decisive for us last season – but have made great investment in players who can give us a great , great future. It is something we have done almost to make sure what happened last year [finishing fifth] does not happen again."