The lawyer, Andres Granados, dropped off the documents at a court in Mexico City yesterday, which he said will hand them over to a panel of appellate judges.
Granados argued that the wrong US embassy official signed one of the extradition requests and that Guzman could face the death penalty if he is put on trial for murder in Texas.
"We know it's a high-profile case, which is very complex because it has to do with Mr. Guzman," Granados told reporters after filing the appeal.
A "college," or panel, of judges will review the appeal but Guzman's lawyers also plan to take the case up to the Supreme Court.
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Guzman is facing two extradition bids, one in California for drug distribution and another in Texas on charges that include murder and money laundering.
When the foreign ministry approved the extradition in May, it said the US government had given "enough guarantees that the death penalty will not be applied."
Guzman's extradition would set up a major trial in the United States for the head of a cartel accused of providing tons of drugs to addicts in the United States while fueling violence in Mexico.
After the slippery drug kingpin was recaptured in January in his northwestern home state of Sinaloa, Pena Nieto demanded his speedy extradition.