The lengthy judgment, read out by a court employee, was televised live nationwide.
"He was the one who was on top of the complainant, who resisted his kisses, pushed him and fought him back until she lost consciousness because of alcoholic drinks she had taken," it read.
It also said that "Nicole", known by her pseudonym in the case, was so intoxicated that she could not have consented to sex, pointing to a testimony that Smith had carried her to a van where the incident occurred.
Judge Benjamin Pozon, who found Smith guilty, also ordered him detained at the Makati jail while Philippine and US officials work out where he should serve his sentence.
The order gave the Makati police custody of Smith, Philippine media reported.
US exit plan
Raul Gonzalez, the Philippine justice minister, said the US intends to take Smith out of the country.
"The US seems to be indicating they want to bring Smith to Okinawa for another trial, trial by the US court," he said on Monday.
He said Smith should be held in Philippine custody, but acknowledged that, under the Visiting Forces Agreement (VFA), the US could seek custody of the convicted serviceman.
He acknowledged that negotiations could turn thorny, saying Manila would insist that Smith remain in the Philippines until his appeal process was exhausted.
"I'm quite hopeful, however, that the US will consider our sentiments," he said.
The case had strained ties between the Philippines and the US.
About 100 protesters outside the court chanted slogans that read "Justice for Nicole, justice for our nation. Scrap VFA", referring to the 1998 agreement that governs joint military exercises with foreign troops.
Critics say the VFA favours the US and grants its troops unfair protection against prosecution.
Smith is the first American soldier to be convicted of wrongdoing in the Philippines since Manila closed down US bases in the early 1990s.