The Greens last triumphed on home soil in 1990, but have now secured another trophy by beating a Senegal side that were looking for their first ever AFCON title.
Algeria made the breakthrough in the second minute of the contest when Baghdad Bounedjah saw his strike from the edge of the Senegal box hit defender Salif Sane before dropping into the back of the net.
It was somewhat of a freak goal with the ball initially looking to be heading over the crossbar, but it was the perfect start for Algeria, who threatened a second in the sixth minute following a dangerous free kick into the Senegal box.
Henri Saivet was the player making things happen for Senegal in the final third, but Les Lions de la Teranga were struggling to fashion clear opportunities. Cheikhou Kouyate did have a half-chance in the 14th minute, although his header from a Saivet free kick drifted harmlessly wide of the post.
Senegal were the better team as the match passed its 20-minute mark, even without star player Sadio Mane seeing much of the ball. Algeria continued to defend well, however, with Riyad Mahrez putting in plenty of defensive work.
Saivet registered a shot on target in the 27th minute from a long-range free kick, but it was a comfortable save for Rais M'Bolhi between the Algerian sticks.
The sheer volume of free kicks was making it difficult for either side to gain the momentum as the first period approached its latter stages, with Algeria fairly comfortable despite seeing little of the ball.
There was certainly a bite to the contest, meanwhile, with Mane and Sofiane Feghouli clashing late in the half and Senegal wanting a second yellow for Ramy Bensebaini following a risky challenge on Sarr.
M'Baye Niang came close to a spectacular leveller for Senegal late in the first half when he struck a brilliant effort towards the top corner from distance, but the ball just moved away at the final moment.
Cisse's team also had a shout for a penalty in the first minute of added time at the end of the half when Sarr went down under a challenge from Mehdi Zeffane, but the referee pointed for a corner.
Tensions boiled over as the two teams left the field at the interval, with a number of players becoming involved in an altercation which eventually calmed down.
The first 10 minutes of the second half passed without incident - Senegal were still enjoying plenty of the ball, but the overall quality from the likes of Niang and Ismaila Sarr was disappointing. Indeed, it was not a surprise when Cisse looked to his bench in the 59th minute, introducing Krepin Diatta for Badou N'Diaye.
Senegal were awarded a penalty on the hour when Adlene Guedioura was adjudged to have handled inside the Algerian box, but the referee consulted the monitor and eventually changed his mind, much to the frustration of Cisse's team.
The team in green were very much on the front foot, though, with Mane and Saivet both sending warnings during a period where Algeria were showing signs of tiredness.
Another big chance arrived in the 66th minute when Niang broke into the penalty box before rounding M'Bolhi, but the number nine fired over the crossbar as Algeria survived another dangerous moment.
M'Bolhi had to make a smart stop to keep out a strike from Youssouf Sabaly in the 69th minute as the pressure continued, with Algeria finding a way to hold onto their lead.
Sarr then had a huge chance down the other end when the ball fell kindly for the attacker - the 21-year-old almost struck his volley too well, though, and it flew over the crossbar.
Cisse's team continued to push for a leveller in the four minutes of added time, but Algeria held on to win the Africa Cup of Nations for the first time since 1990, sparking wild celebrations at the final whistle.
SENEGAL (4-2-3-1): Gomis; Gassama, Sane, Kouyate, Sabaly; Gueye, Ndiaye (Diatta 59'); Mane, Sarr, Saivet (Diagne 75'); Niang (Balde 85')
ALGERIA (4-4-2): M'Bolhi; Zeffane, Mandi, Benlamri, Bensebaini; Mahrez, Bennacer, Guedioura, Feghouli (Jean-Tahrat 85'); Belaili (Brahimi 84'), Bounedjah (Slimani 89')