Yudhoyono, being a former general, also comes from a military that has a strong musical tradition.
"Presidents have all kind of hobbies, there are presidents who like to play saxophone, the prime minister of New Zealand likes to climb mountains, there are presidents who like fishing, my hobby is music," he said.
He wrote one of the songs in the album while returning home from the Asia-Pacific Economic Co-operation summit in Sydney, Australia, in September.
Four other numbers were performed during last Ramadan's breaking-the-fast gathering at Yudhoyono's private residence in Cikeas, West Java.
The songs were recorded by noted Indonesian singers including Ebiet G Ade, Bimbo, Widhy AB Three and Andien.
Andi Mallarangeng, a presidential spokesman, said composing songs was Yudhoyono's "way of refreshing, relaxing everywhere he goes during his busy schedule".
The president is not the first former military officer and politician to make a foray into the music industry.
General Wiranto, the one-time armed forces chief, had also released an album during his failed presidential campaign.