Childress Racing also said Caterpillar will remain Burton's primary sponsor.
The racing team didn't reveal how long the contract is for or how much Burton will be paid.
Burton has been associated with Childress Racing since August 2004 and qualified for the Chase for the Sprint Cup championship four of the last five years.
"I'm excited to continue my relationship with both Richard Childress and Caterpillar," Burton said in a statement. "Continuing my career at RCR was a top priority for me, and it's great to have the support of Caterpillar behind us."
Burton is off to a slow start this year, failing to finish in the Top 10 in any race and lagging in 22nd place in the standings.