Khan told undercover FBI agents or informants about a desire to join Muslim insurgents, and discussed guns, training and preparing for a Third World War, prosecutors said.
Khan's guilty plea "should serve as a sobering reminder that we need to remain vigilant in our efforts to detect and root out terrorism, even in our own backyard," U.S. Attorney Robert Pitman said.
Khan lived with his family in the Austin suburb of Round Rock. Authorities had said Khan was in conflict with his parents after someone told them he was interested in jihad. Sentencing was not immediately set.
Khan's guilty plea came a week after another Central Texas man, Michael Wolfe, who prosecutors called Khan's co-conspirator, also pleaded guilty to terror charges in a separate case.
Authorities said Wolfe sought to join an al-Qaida splinter group leading militants in Iraq. He was arrested in June at George Bush Intercontinental Airport in Houston as he was leaving for Turkey with his wife and two young children.
A spokeswoman for Khan attorney Kevin Collins confirmed the guilty plea but offered no further comment.