He arrived at 9:30 p.m. Tuesday at a San Salvador airport.
Alvarenga was in a wheelchair and appeared tired and weak. He was given a microphone, but did not speak to the crowd of journalists and travelers, La Prensa Grafica said.
"I do not know what to say," he said.
He was taken to the hospital where doctors will complete lab tests and checkups, CNN said.
Alvarenga and his family have asked for privacy since he was found on Jan. 30.
"He doesn't know what it is like to be a celebrity, or how to respond to all the media attention," Irene Sanchez, a spokesman for El Salvador's Foreign Ministry, said.
He told rescuers he and a companion set off from Mexico on a one-day fishing trip in late 2012. Blown off course and caught in a storm, they eventually lost their engines. The teenage companion died of starvation about a month later.
After being adrift at sea for more than 13 months, islanders found Alvarenga in a heavily damaged boat near a remote area of the Marshall Islands, thousands of miles from where he began.
He said he had been living off fish and turtles, and been drinking rainwater and his own urine.