The 43-year-old Sky assistant died of a severe bacterial infection which developed into sepsis, the team said in a news release.
Gonzalez suddenly became ill on Sunday and was taken to hospital in Seville.
"We are devastated to report Txema tragically passed away on Friday evening in hospital in Seville," said team principal Dave Brailsford.
"His close family were with him."
Gonzalez's condition had nothing to do with the sickness that affected all of the British team's riders on the Tour of Spain, added team doctor Steve Peters.
Spanish rider Juan Antonio Flecha pulled out during Friday's seventh stage due to a high fever and upset stomach.
Two of his Sky team mates, Briton Ben Swift and South African John Lee Augustyn, withdrew from the race on Monday.
An ex-amateur rider with the former top Spanish team KAS, Gonzalez worked with ProTour teams Euskaltel-Euskadi and Saunier Duval before joining Sky for their debut season this year.
There will be a minute's silence in memory of Gonzalez at the start of Saturday's eighth stage.