The former FC Twente man signed a four-year deal with the Saints this week as the South Coast club reinvested some of the £25m received from Lallana's move to Liverpool.
"We're very happy that Tadic is coming in. He's a great player," he told the club's official website.
"He's 25 and he has a great future, and I think he can now reach the level that we need and a player needs to be at in the Premier League.
"When we lost a great player in Lallana, we were looking for a similar player in that position, and we've found it."
Tadic signed on for a fee in the region of £10m.