The bodies of the 36-year-old volleyball star and her 57-year-old husband were discovered half buried in a lemon grove, in Alquerías, a village about 12 kilometres from the city of Murcia.
The couple were reported missing by family on May 15th after they failed to return to the Netherlands. They were last sighted on the afternoon of May 13th when they checked into Murcia's El Churra hotel.
Their rental car was found nine days later on a street in the southeastern Spanish city, news agency AFP said on Monday.
Their disappearance sparked intense media interest in the Netherlands and volunteers plastered the streets of Murcia with posters calling for information about the whereabouts of the pair.
Murcia police chief Cirilo Duran told a press conference that all the "outward signs" suggested that the bodies found belonged to the missing couple, but added that police are still awaiting results from a DNA analysis to confirm the findings.
"What is clear is that it was a violent death," he said.
Duran said three people have been arrested in the case.
La Verdad de Murcia also cited sources as saying that "the people arrested have links with organized crime".
Visser — famous in the Netherlands — was a former volleyball player with the Dutch international squad and had been capped on more than 500 occasions.
From 2009 to 2011, she played for Spanish team CAV Murcia 2005. She had also played for CV Tenerife and Cantur Las Palmas.