The Milton Keynes-based team announced last week that Ricciardo will be the man to replace the outgoing Mark Webber at the end of the campaign.
The Australian has picked up 18 points for Toro Rosso this season but Vettel predicts that he will be competing for the title with a better vehicle next term.
Red Bull considered handing a contract to Lotus' Kimi Raikkonen but opted to go for the younger man as they look to build a Championship team for the future.
Vettel said: "I'm sure he will try very hard to give me a hard time and I will try to do the exact same thing.
"Next year there's a lot of work ahead and we are both looking forward to the new stuff that is coming.
"We know it's a lot of work but hopefully we have a competitive car and can prove that we are hopefully two of the best."