"Laboratory results of all 13 persons are negative for unsafe infectious diseases, and they will be discharged from the hospital as soon as possible", officials said in a statement.
They also posed with a drawing of former Thai navy SEAL Petty Officer Saman Gunan, the sole fatality of the rescue operation, and wrote messages of thanks to Saman.
In another video Thai officials released this week to share the group's progress, the boys were shown smiling and waving from their hospital beds without speaking. Officials are specifically anxious about any possible mental duress suffered by the team's coach, 25-year-old Ekkapol "Ake" Chantawong, ABC News reported. Some of the boys appear to be crying in the photos.
Doctors also said they are getting ready to do another psychological exam on the boys after some spent as many as 18 days isolated in the cave. They were not told of SEAL Saman Kunan's death until Saturday.
The rescue bid was also lauded for the hard, long hours and teamwork between highly-skilled Thais and foreigners.
He was ordered the Knight Grand Cross (First Class) and given the medal of the Most Exalted Order of the White Elephant.
FIFA, world football's governing body, had invited the boys and their coach to attend the final in Moscow, but they could not go for medical reasons.More news: Mexico elections center on disgust with corruption, violence
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The rescued Thai soccer team will watch a recording of Sunday's World Cup final between France and Croatia rather than the live broadcast so the 12 boys and their coach can rest.
Officials at Chiangrai Prachanukroh Hospital told reporters at Saturday's press conference that all 13 are tentatively scheduled to be discharged Thursday.
The 12 boys ages 12-17 and their 25-year-old coach had gone exploring after a practice June 23, but heavy rains flooded the cave and trapped them more than 2.5 miles from the entrance.
The footage of the boys from a Saturday news conference shows them still wearing surgical masks, a safeguard against infection since the last of them was pulled from a cave on Tuesday after being trapped for nearly three weeks.
The boys, aged 11-16, were pulled from the cavern by Thai Navy Seals and foreign cave diving experts, in a three-day rescue push that ended on 10 July.
While the cave system has been closed, officials have said it could be reopened as a tourist attraction - with strict safeguards to prevent future disasters.