Gen Martin Dempsey said the "vast majority" of documents taken by the ex-NSA contractor were military-related.
Since last year, news organisations have published dozens of stories based on the leaked intelligence documents.
Mr Snowden faces spying charges in the US but has been given asylum in Russia.
Gen Dempsey, chairman of the joint chiefs of staff, told the House armed services committee on Thursday that a mitigation task force had been established to investigate the extent of Mr Snowden's theft and to determine how to overcome it.
"We're working our way through that which we believe he has exfiltrated," Gen Dempsey said. "And we have, I think, a fairly significant amount of knowledge in that regard.
"The vast majority of [the pilfered documents] were related to our military capabilities, operations, tactics, techniques and procedures."
Gen Dempsey said the "magnitude of this challenge" suggested the task force would need to run for about two years.
"I suspect it could cost billions of dollars to overcome the loss of security that has been imposed on us," he said.
Mr Snowden, a former technical contractor for the National Security Agency who fled from the US in June, faces espionage charges in the US.
It will take the US two years and possibly billions of dollars to overcome the harm done by Edward Snowden's intelligence leaks, the top-ranking US military officer has said.