There was no official confirmation of Aoun's announcement, but opposition sources said Khoury had won by a margin of about 500 votes from around 75,000 cast.
Amin Gemayel said: "I don't recognise the unofficial result, there was vote-rigging."
Earlier, unofficial results showed pro-government candidate Mohammad Amin Itani winning by a large margin in the Sunni Muslim seat of west
Beirut which became vacant after the killing of Eido in June.
Fuad Siniora, Lebanon's prime minister, hailed the peaceful by-elections as a civilised response to political assassination.
In a statement he said: "Democracy in Lebanon will defeat terrorism."
The contest is seen as the latest part of the country's ongoing political crisis.
Gemayel, a Christian cabinet minister, was shot dead in November, while Eido was killed in a June bombing. Both were government supporters.
The vote in Gemayel's Metn seat has divided the community and could escalate the country's political stalemate.
Thousands of troops and police were on duty in Metn, but no incidents were reported and turnout was said to be around 45 per cent.
A nine-month political struggle has already caused the worst internal violence since the 1975-1990 civil war, and some feared a fresh outbreak of violence during voting.
Observers say the official election outcome, due to be announced on Sunday evening, will be an indicator as to which way the Christian camp is leaning ahead of an election to replace Emile Lahoud, the president.
The government and opposition remained at odds over the vote itself after Fuad Siniora, Lebanon's prime minister, called Sunday's poll without the approval of Lahoud.
Nabih Berri, the parliamentary speaker, and an ally of the Hezbollah-led opposition said he would not acknowledge the poll results.
The vote in Metn for Gemayel's seat had been fiercely contested.
Syria has denied any involvement in the killings
of Walid Eido, left, and Pierre Gemayel [AFP]
Amin Gemayel, Lebanon's president for much of the 1980s, decided to compete for his son's seat on behalf of the ruling party.
He stood against Khoury, who is supported by Aoun, a former army commander and prime minister allied with the opposition.
His party dominated in legislative district elections in 2005.
"Our main goal is participation [in government]. We extend our arm to all the Lebanese to rebuild Lebanon and to salvage it from this big crisis," Khoury said.
Alain Aoun from Khoury's Free Patriotic Movement told Al Jazeera that the party is not aligned to Syria or Iran.
"We are trying to build bridges in Lebanese society, including Hezbollah which are the representatives of the Shia, because we want to solve the crisis in Lebanon through dialogue."
Gemayel said his party aimed to "complete [Lebanon's] sovereignty, confirm Cedar Revolution and accomplish the goals of the independence uprising," in reference to mass street protests that forced Syria to end its 29-year military presence in Lebanon in 2005.
He accuses Syria of orchestrating the killing of Pierre Gemayel, Eido and other anti-Syrian figures.
Damascus denies involvement.
Mohammed al-Amin Itani of the ruling majority is expected to replace Eido's Beirut seat since the opposition did not officially sponsor a candidate.
The standoff between Siniora and the opposition threatens to tear the country apart and could lead to the formation of rival government factions if parliament fails to elect a new president before the deadline for Lahoud to step down on November 23.
In Metn, giant pictures of Gemayel and his son were had been displayed, particularly in their homebase of Bikfaya, where voters cast ballots before heading to the cemetery to place a white rose on Pierre Gemayel's tomb.
"We feel we are in danger because of the Syrian-Iranian axis," said Eliane Haddad outside a polling booth.
"We want to tell everybody that we are with the Gemayels, we are with Lebanon's independence and we are here to stay."
Fadi Nasr, an Aoun supporter, said: "We are proud of our alliance with Hezbollah because it has made our lives easier in terms of living together in peace, Christians and Muslims."