The wooden coffin containing the body of Gaid Salah, who died of a heart attack on Monday aged 79, arrived at 0630 GMT, covered in a national flag and carried by officers.
Surrounded by large numbers of motorcycle outriders, the funeral procession converged on the palace, which was built in the 18th century for Ottoman governors, Presstv Reported.
Gaid Salah became the country's de facto strongman after longtime president Abdelaziz Bouteflika was forced to step down in the face of huge street protests in April.
Interim military chief of staff Said Chengriha was in attendance, while President Abdelmadjid Tebboune arrived a little after the procession.
Tebboune won a December 12 presidential election with 58.1 percent of the vote on a turnout of less than 40 percent, according to official results, in a poll dismissed by protesters as a ploy by Gaid Salah and other establishment figures to consolidate their power.
After his win, Tebboune awarded Gaid Salah the National Order of Merit, Algeria's highest honor. After the general's death he announced three days of national mourning.
Abdelkader Bensalah, interim president after Bouteflika's fall, and other senior personalities also gathered in front of the coffin.
Images broadcast by several TV stations showed a crowd massed at the gates of the palace to pay their final respects to Gaid Salah, who served as army chief for 15 years.
State TV later played images of small groups of civilians entering the palace complex and briefly stopping in front of the coffin to pay their respects.
The religious affairs ministry asked imams to lead prayers in Gaid Salah's memory on Wednesday.
He was due to be buried shortly after 1200 GMT in Martyrs' Square in Al-Alia cemetery, where former presidents and other major Algerian figures are laid to rest.