It's claimed Saints refused to cough up huge fees to intermediaries as part of the transfer.
Pochettino said: "I am very pleased to have secured the signing of Victor because we are a big admirer of his talents and he will fit in well to the team here at Southampton.
"I want to stress that the deal could have been done sooner, but this shows that we do business on our terms. The most important thing that ourselves, Celtic and the player are all happy with the way it has all gone.
"The fact that a lot of top European clubs were also keen to sign him shows what an attractive prospect Southampton Football Club is to a player who had his pick of the teams in England and abroad."