Vertonghen sealed his £9million move to Tottenham yesterday after passing a medical.
The Belgium international is likely to form Spurs' first-choice central defensive partnership with Dawson next season, particularly with the likely retirement of stalwart Ledley King.
"I hadn't seen much of him [Vertonghen] before but from what I have seen in the first two or three days he will be a good signing," said Dawson.
"But we've got a big squad. Younes [Kaboul] was brilliant last season. Everyone is fighting for their position. It's a position where you get roughed up a little bit so you need a big squad."