David Higdon, NASCAR communications vice president, told reporters that Busch "has agreed to our terms and conditions that must be met before he is eligible for consideration for reinstatement of his NASCAR license." Higdon said Busch agreed to the conditions last week.
Higdon did not say what Busch would need to do before being reinstated by NASCAR.
Busch's team, Stewart-Haas Racing, applauded its driver's decision.
"Kurt's willingness to embrace the conditions set forth by NASCAR is a positive step that we support," the team said in a statement.
Busch was suspended indefinitely by NASCAR on Feb. 20 after a Delaware family court judge said the 2004 Cup champion "more likely than not" committed domestic violence against his former girlfriend, Patricia Driscoll.
Judge David W. Jones made the remark in his decision to grant Driscoll a no-contact order against Busch.
A "preponderance of the evidence" showed Busch abused Driscoll by "manually strangling" her and smashing her head against a wall inside his motor home during an argument at Dover (Del.) International Speedway last September, Jones' filing stated.
Driscoll's allegations against Busch also are being weighed by the Delaware attorney general's office, which has yet to decide whether to prosecute Busch on criminal charges.
Busch, 36, initially appealed his NASCAR suspension, but was unsuccessful in two attempts to be reinstated. He was forced to sit out of the Daytona 500 after qualifying for the race.
Regan Smith, who drove Busch's No. 41 Chevrolet in the first two Sprint Cup Series races, will drive again for Stewart-Haas Racing at Las Vegas Motor Speedway this week.