Ozil joined Arsenal for a club-record fee of £42.5m on the final day of the transfer window last week, becoming manager Arsene Wenger's first and only big signing of the summer.
Villas-Boas was in no doubt as to Ozil's quality, but questioned whether Arsenal needed to strengthen their midfield with Jack Wilshere, Santi Cazorla, Mikel Arteta and Thomas Rosicky all playing similar roles to the German.
"He is a wonderful, gifted footballer and in the end Arsenal paid heavily for a player of that dimension," Villas-Boas told PA.
"It's a €50m transfer for a number 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."
Spurs were understood to be upset at Madrid for selling Ozil to their North London rivals given the good relationship that they had cultivated with the Spanish giants, but Villas-Boas admits that his side have no control over Madrid's transfer dealings.
"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," he added.
Tottenham brought in seven international players during the transfer window for a combined fee of more than £100m.