The swap will take effect prior to next weekend's event at Richmond International Raceway.
The crews will remain as is for this weekend's race at Talladega Superspeedway.
As a result, starting next week Todd Berrier will move to Mears' No. 07 after spending more than five years as Harvick's crew chief on the 29. The pair won eight Sprint Cup races together, including the 2007 Daytona 500.
Gil Martin will move to Harvick's team. Martin directed the No. 07 team to two consecutive Chase for the Sprint Cup appearances with driver Clint Bowyer.
"The decision to interchange the 29 and 07 teams was made to make both programs stronger and more successful," RCR president and CEO Richard Childress said in a statement. "Our main objective has always been to have all four of RCR's teams qualify for the Chase for the Sprint Cup. Neither team has had the success this season that we know they're capable of, so we decided it was time to make a change to improve the two teams and the overall strength of RCR. We feel this change positions us to achieve that goal.
"Todd and Gil are proven winners who have strong and successful teams behind them. Chemistry is an important part of any successful organization and I felt it was time to change the makeup of these two teams. We've done this before with positive results," he said.
Marty Smith covers NASCAR for ESPN.com.