Ozil joined the Gunners from Real Madrid in a £42.5m deal on deadline day last week, becoming manager Arsene Wenger's first major signing in a summer that saw Spurs splash over £100m on seven international players.
Villas-Boas believes that his side and Manchester City did the best business of the teams chasing a Champions League spot, although he did concede that Arsenal did well to capture a player of Ozil's quality at such a late stage.
"All of us have done good business in the transfer window, but Manchester City and us maybe a little bit more than Manchester United, Chelsea, Arsenal and Liverpool," Villas-Boas told PA.
"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."