Zoltan Forai, 44, was arrested Friday afternoon after police officers patrolling the area spotted him drinking beer on the corner of Woodhaven Boulevard and Myrtle Avenue near the park's Victory Field, less than half a mile from where the body was found.
Police also found a marijuana joint in his pocket, according to the criminal complaint.
On Saturday, Forai, whom authorities said was homeless, was charged with second-degree murder and criminal possession of a weapon, police said.
The body of the victim, identified as Diego Piedrahita of Booth Memorial Avenue in Flushing, was found near Park Lane South and Woodhaven Boulevard by two parkgoers on June 10 around 3:30 p.m., officials said.
Police said the men saw a trail of blood leading to the victim who was lying with severe head injuries under a bridge near abandoned railroad tracks.
The medical examiner determined that Piedrahita suffered multiple skull fractures and ruled his death a homicide.
According to the criminal complaint, Forai kicked Piedrahita repeatedly in the head and other parts of the body. He then hit him multiple times in the face and head with a rock, causing multiple fructures.
Police found a blood-stained tree branch, which they suspect was also used as a weapon, authorities said.
The motive for the crime remains unclear, officials said, adding that Forai and the victim both frequented the park and knew one another. They also said Forai had been seen around Victory Field in the past.
Information about Forai's attorney was not immediately available.