Fellow forward Helder Postiga also scored twice and Miguel Veloso got another for the home side in the last 20 minutes to wrap up the victory after a 0-0 draw on a swampy pitch in the first leg in Zenica last Friday had left the tie wide open.
Portugal started strongly and Ronaldo showed his intent in the fifth minute with a shot that visiting goalkeeper Asmir Begovic struggled to block.
They were two goals ahead by the half-hour mark thanks to a trademark Ronaldo long-range free-kick after eight minutes and a delightful Nani shot from more than 30 metres in the 24th.
"I think people are now used to me scoring from free-kicks and it's become one of my specialities," said Ronaldo.
The world's most expensive player was dangerous throughout and had many chances to crown his display with a hat-trick.
The Portuguese went on to dominate the match, their solid defence led by the imposing Pepe while their flowing midfield gave little room for the Bosnians to manoeuvre.
The visitors were toothless in attack against a solid defence for the first 40 minutes but they were given a lifeline when Fabio Coentrao handled in the area and playmaker Zvjezdan Misimovic slotted in from the spot to make it 2-1.
Ronaldo sidestepped the keeper to score his second goal after 53 minutes and although the Bosnians had Senad Lulic sent off a minute later, Emir Spahic's 65th minute goal gave them brief hope before Postiga and Veloso struck.
The Bosnians, also beaten by Portugal in a play-off for the 2010 World Cup, will be disappointed to miss out on qualifying for their first major finals but their key players, like striker Edin Dzeko and Miralem Pjanic, failed to raise their game.
"Congratulations to Portugal, they played faster and better, and I want to wish them good luck in the Euros," said Bosnia coach Safet Susic.
Portugal's qualification follows a remarkable revival under coach Paulo Bento who took over after their dismal start to the campaign and guided them to five straight wins before defeat in the final group match with Denmark left them in the play-offs.
Appointed last year to replace Carlos Queiroz, who was sacked for insulting anti-doping agents, Bento was under immediate pressure after Portugal had taken just one point from two qualifiers but he bonded with the squad very quickly.
"Qualification was always the objective, but in a difficult context after the first two games as we had no room for error," said Bento, whose knowledge of the players and recent experience as a Portugal international helped to revive their fortunes.
"What leaves me most proud and pleased is that we did so with a strong team spirit," he added.
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