Ferrari have undergone a major overhaul in recent weeks with four-time world champion Vettel coming in to replace departing Spaniard Fernando Alonso and Maurizio Arrivabene succeeding sacked Team Principal Marco Mattiacci.
Raikkonen, who won Ferrari's last world title in 2007 during a previous spell with the team, ended his disappointing 2014 season with a day of testing at Abu Dhabi before returning to the team's Italian base at Maranello.
Vettel, who won four consecutive world titles with Red Bull before deciding to join Ferrari on a three-year deal, spent a day at the Ferrari garage in Abu Dhabi.
"It was nice that he joined us in the garage for the first day of testing, although I have to say that didn't surprise me, because I know what he's like and his approach to work," Raikkonen said in a team statement.
"I think we can enjoy ourselves on track together, both of us fighting to be ahead of the other, while also working as a team to reach the common target of progressing in order to get the Scuderia back to the level it should be at."
Raikkonen said testing had "produced a lot of useful data" as the team set about producing a more competitive car for next year.
Ferrari finished the season winless for the first time since 1993, with former two-time world champion Alonso finishing sixth in the drivers' standings over 200 points behind British champion Lewis Hamilton.
"I am sure that thanks to the knowledge we acquired over the course of the season, we will be able to develop a more competitive car," added the Finn, who finished 12th overall on just 55 points.
"Clearly, how much progress we make depends on the time available and the possibilities presented by the regulations, which for the moment, impose certain limits for everyone, but I have every confidence in the ability of the team."