Barrow, whose shock victory this month ended the 22-year rule of Yahya Jammeh, said the country's chief of the defence staff had called to pledge the army's backing.
"He said the security of this nation is assured by the armed forces," said the 51-year-old estate agent. "He said he was loyal to President Yahya (Jammeh) because he was the elected president.
"He said now that I am elected in to office by the Gambian people, he will support me," he added.
Barrow was elected as president of the smallest country in West Africa after he beat incumbent President Yahya Jammeh in the December 1 polls.
Asked if he will prosecute those accused of human rights violations over the last 22 years, Barrow said: "We will look at what was happening in the past.
A "Truth and Reconciliation Commission is very important here and we have seen it happened in South Africa. We will establish a Truth and Reconciliation Commission to look at the past."
The UN envoy to West Africa Mohamed Ibn Chambers said last week that the United Nations will help the incoming government to establish such a commission.
Barrow said he had not yet met the outgoing president, but said his officials were working on the arrangements.
"This transition issue is a new thing in Gambia and both teams (the ruling party and opposition) are not experienced on it," he said, adding that he hoped to set a date for his inauguration "very soon."
Latest official figures gave Barrow 43.29 percent of the votes in the presidential election, while Jammeh took 39.64 percent. The turnout was at 59 percent.
Meanwhile Thursday a Gambian appeal court granted bail to 11 political activists detained since April for holding rare protests, a judicial source said.
Their lawyer Antouman Gaye noted that they were members of the United Democratic Party (UDP), of which Barrow was the presidential candidate.
UDP founder and leader Ousainou Darboe, who was jailed in July for taking part in a protest, was freed on bail with 18 others on Monday, as part of their ongoing appeal against three-year sentences.