Spurs have announced the appointment of the Italian, who has made a name for himself as a serial winner during spells at Juventus, Chelsea and Inter Milan.
Conte is always very keen to get his own way though, and it's understood a lack of assurances over funds in the transfer market led to his departure at Inter Milan just weeks after leading the Serie A club to their first league title in over a decade.
A lack of signings in his second summer at Chelsea also begun his road to an exit at Stamford Bridge, after winning the Premier League title and the FA Cup in two years in charge.
Backed by Spurs' billionaire owner Joe Lewis, chairman Daniel Levy has run the club's finances very smartly since being at the club from 2001, but a perceived lack of spending on transfers has been a gripe for fans.
But Redknapp believes the club will be spending at the first opportunity under their new boss, saying Conte wouldn't have taken the job otherwise.
Speaking to talkSPORT Breakfast, the former Tottenham manager said: "I can see them spending.
"I don't think he'd have come if he couldn't improve the team. That was probably one of the provisions of him coming.
"They're not a poor club. Joe Lewis, people don't realise how wealthy the owner of Tottenham is, he's up there with one of the richest men in the world.
"They can afford to bring players in and I think they will do that for sure."
A mammoth task awaits Conte, who takes over a Tottenham side that's ninth in the Premier League and in very bad form, although they are only five points off the top four after 10 games.
Redknapp believes the Italian will succeed to guiding the club into the Champions League spots this season despite their poor start to the campaign.
He added: "When you look at the place, the stadium with 60,000 people in it is just incredible, there wouldn't be a better training ground, it's all in place.
"As a manager you're looking at it and thinking they can't get much worse… and Conte will be coming in be thinking that maybe he can grab that fourth spot this season.
"He's not going to get first, second or third because those three teams - Chelsea, Liverpool and Man City - are on another level, but I think they can finish above Man United, West Ham and Arsenal and get that fourth spot.
"They've got good players. If he can get Harry going again, if he can wake Dele Alli up, what a talent, there's an incredible player there and someone needs to get him going… Heung-min Son, Lucas Moura, they're full of talent.
"Let's hope he can come in and get these players doing what they're capable of doing."