Chris Martin has been scootering around L.A. illegally ... sometimes with his kid on the back seat ... but today, the Coldplay singer raced down to the DMV to finally get a valid license to drive in California, TMZ has learned.

Multiple DMV sources tell us ... records show Martin has never obtained a CA driver's license, despite the fact he's been tooling around town on his Vespa for weeks.

The license issue just came to light after his wife Gwyneth Paltrow dangerously cut off a school bus on a Vespa -- while her daughter Apple was on the back seat. It was later revealed that GP didn't have a motorcycle license at the time of the incident.

Paltrow raced to the DMV days later and passed her tests -- and today, her husband followed suit.

Martin was spotted at the DMV in Santa Monica on Wednesday -- with his Vespa -- and good news, HE PASSED HIS TESTS (we're told) ... so all is well.

Now check your mirrors and proceed with caution.