The authority to do this appears to be based around a blend of legal decisions. The Supreme Court has ruled that police can search your phone if they have a warrant, and that they can order you to produce fingerprints without a judge's approval. However, it's not certain that you can combine the two.

As the LA Times explains, there's a dispute as to whether or not using your fingerprint to unlock your phone is a violation of the Constitution's 5th Amendment, which protects against self-incrimination. While a fingerprint isn't the same as testifying, unlocking your phone could be treated that way. Even with precedent from a 2014 Virginia case (which determined that fingerprints are okay, but passcodes aren't) working in the feds' favor, there's no guarantee that police can order fingerprint access going forward.