Ms Alvarado and her sister Sofia Trinidad, 23, vanished on Thursday after being seen leaving a party near the northern city of Santa Barbara.
She had been due to compete in the upcoming Miss World contest in London.
Plutarco Ruiz, said to be the boyfriend of Ms Trinidad, was detained along with another man, Aris Maldonado.
The two women’s bodies were found in Cablotales village, near the River Aguagua, National Bureau of Criminal Investigation chief Leandro Osorio said.
Weapons and a car were seized, he added, and a “protected witness” has provided valuable information.
The two women were last seen alive in a car without a licence plate as they left a birthday party on 13 November.
According to Reuters news agency, the two men arrested are believed to be the last people to have seen the young women before they disappeared.
“Both are being questioned as part of the investigation into the disappearance of [Ms Alvarado] and her sister,” police spokesman Jose Coello said.
“We hope to establish what role they may have played.”
According to a UN report, Honduras has the world’s highest homicide rate, with 90.4 people murdered per 100,000 of the population
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