Police had confiscated the passports of the couple - who were reportedly on their honeymoon - as they were investigated for taking part in a public assembly.
Spanish media identified them as Dani Cuesta and his wife Mireia Saez, supporters of Spanish first division team Valencia.
Cuesta had posted photos of himself on social media from several locations in Singapore holding a black and yellow banner that read "Lim go home", including outside a building where the businessman is believed to live.
Both were stopped at the airport on Oct. 4 when they attempted to board a flight to Bali, Valencia mayor Maria Jose Catala had told Spanish radio station Onda Cero.
In a statement Tuesday, police said they issued a "stern warning" to a 34-year-old man for "taking part in a public assembly without a permit... and for affixing notices".
A 30-year-old woman was also warned "for the offense of abetting the Spanish man's participation in a public assembly".
"The two Spanish nationals have since departed Singapore," police said, without saying when.
Singapore has strict laws limiting critical speech and assembly, which includes protests by just one person.
Lim, one of Singapore's richest men, bought debt-ridden Valencia in 2014, becoming the Spanish side's first foreign owner.
While his arrival was initially enthusiastically received, he has failed to improve the club's fortunes and many Valencia fans have turned against him.
Protests against Lim have become commonplace in Valencia, with banners saying "Lim go home" regularly displayed at La Liga games at the club's stadium.
Valencia are currently 18th in the league.