The process can still be appealed, meaning it could be weeks or months before the Sinaloa cartel leader may be sent to the U.S., where he is wanted in multiple jurisdictions on charges related to drug trafficking and organized crime.
Guzman's lawyers now have 30 days to appeal the decision, and they have said they will.
The department said Friday in a statement that the United States has provided "adequate guarantees" that Guzman would not face the death penalty.
Mexico has abolished capital punishment and does not extradite its citizens if they face possible execution.
Friday's ruling covered an extradition request from a Texas federal court related to charges of conspiracy to import and distribute cocaine and marijuana, money-laundering, arms possession and murder, and another extradition request from a federal court in California.
In all, Guzman faces charges from seven U.S. federal prosecutors including in Chicago, New York, Miami and San Diego.
Jose Refugio Rodriguez, one of Guzman's lawyers, said Friday the legal team planned to appeal the decision all the way to Mexico's Supreme Court, and possibly to international tribunals.
Rodriguez told the Milenio television station that any extradition would take "at least one to three years."
"We expected it," Rodriguez said of the foreign relations department decision.
"It is no surprise."
Rodriguez said Guzman knew about the ruling and said he was "calm."
"He knows and is conscious that the real battle against extradition is going to be waged through the constitutional appeals process," Rodriguez said.
Guzman was arrested in January after almost six months on the run following his escape from a maximum-security prison through a mile-long tunnel that opened to the floor of his shower.
He had already escaped once before in 2001 and spent more than a decade as one of the world's most wanted fugitives until he was recaptured in 2014.
Guzman's lawyers have so far waged a public-relations offensive, speaking to the press and even organizing protests; but as extradition draws nearer, the battle could turn violent, like the one Colombian drug lords waged extradition in the 1980s, said Mike Vigil, a former head of international operations for the U.S. Drug Enforcement Administration.