Red Bull said Ciaron Pilbeam, who has worked with Webber since 2007, had taken a new role at Lotus while Raikkonen's 2012 race engineer Simon Rennie had moved in the opposite direction to team up with Webber.
Rennie was previously a race engineer with double world champion Fernando Alonso at Renault, the team that is now Lotus, as well as Poland's Robert Kubica.
Last season he was famously rebuffed by 2007 champion Raikkonen, who told him over the radio that he knew what he was doing and to leave him alone while on his way to winning the Abu Dhabi Grand Prix.
Lotus later gave all their employees T-shirts with "Just leave me alone, I know what I'm doing" written on them.
Drivers spend much of their grand prix weekends with their race engineers, working together on the set up of the car and strategy.
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