Volker Finke's men went into the game on the back of a 0-0 draw in the first leg in Rades last month, and knew that defeat would see them fail to qualify for only the second time since 1986.
However, the hosts were never really in danger as they produced a dominant performance to become the third African nation to reach the 2014 finals in Brazil.
Fenerbahce striker Pierre Webo opened the scoring after four minutes with a cool finish from close range.
Benjamin Moukandjo doubled Cameroon's advantage with a fine individual goal, but the home fans were given a scare when Ahmed Akaichi pulled one back for Tunisia shortly after half-time.
However, the tie was settled by Jean II Makoun, who scored a second-half brace to spark jubilant scenes at the Stade Omnisport Ahmadou Ahidjo in Yaounde.
Cameroon made three changes from the first leg, with Tottenham defender Benoit Assou-Ekotto and Nancy attacker Moukandjo among those to come in.
Fakhreddine Ben Youssef replaced Sami Allagui in attack for Ruud Krol's visitors, while defender Karim Haggui came in for Alaeddine Yahia.
It did not take the hosts long to open the scoring, Webo capitalising on some sloppy Tunisian defence with a clinical finish across Moez Ben Cherifa.
Cameroon continued to push forward in a bid to kill the tie off, and came close to doubling their lead 10 minutes later when Ben Cherifa was forced into a fine save to deny Assou-Ekotto from long range.
Finke's side were rewarded for their positivity on the half-hour mark as Moukandjo weaved past several Tunisia defenders before firing a low shot beyond Ben Cherifa to put Cameroon in command.
The visitors should have pulled one back shortly before the break, but Syam Ben Youssef headed over from point-blank range.
Tunisia did put themselves firmly back in the tie six minutes into the second half, substitute Akaichi firing home on the half-volley after breaking through the Cameroon backline.
Krol's men began to dictate proceedings following their goal, and had a claim for a penalty turned down on the hour mark after Assou-Ekotto's clumsy challenge on Fakhreddine Ben Youssef.
Just six minutes later Assou-Ekotto proved to be the creator for the goal that all but ensured Cameroon's place in the finals, Makoun heading in a pinpoint near-post corner to delight the home fans.
Moukandjo was denied his second by Ben Cherifa, but Makoun put the gloss on a superb display four minutes from time as he slotted into an empty net after Maxim Choupo-Moting had hit the post.
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