Moeen tested positive upon arriving in Sri Lanka and will continue his 10-day self-isolation in a separate wing of the visitors' team hotel in Hambantota.
Fast bowler Chris Woakes, who was deemed a possible close contact of Moeen, was among those who returned a negative result on Wednesday but will continue to isolate in his room as a precaution.
The England squad will be tested again on Thursday.
"All PCR tests from yesterday are negative, except for Moeen Ali, and we can start controlled training this afternoon," an ECB spokesman said.
England bowler James Anderson says the squad has been made to feel safe by the strict coronavirus protocols in place in Sri Lanka
England's training session on Wednesday will be their first since arriving in Sri Lanka.
The first Test of the two-match series against Sri Lanka starts in Galle on January 14.
Their series in Sri Lanka will be followed by four tests in India in February and March.