A 56th-minute goal by Raul Meireles earned a 1-0 win in the second leg in Bosnia on Wednesday, giving Portugal a 2-0 aggregate victory.
"Finally the angst is over, now yes, we are there," said the tabloid 24 Horas.
Many observers had been critical of coach Carlos Queiroz but several changed their tune after Portugal clinched their place in next year's finals in South Africa.
"How this Portugal team has grown. In a tough match, a boiling atmosphere, on a terrible pitch, they showed maturity. There was soul, concentration ... a true team," said commentator Manuel Casaca in sports daily O Jogo.
Queiroz said he had accomplished "a lifelong dream after a journey of many years".
The coach, in a previous spell in charge, failed to lead Portugal to the 1994 World Cup finals and would have been under intense pressure if they had missed out this time.
Sports Secretary Laurentino Dias, who attended the match in Zenica, congratulated the team on an excellent performance and said qualification would help the combined Portugal-Spain bid to host the 2018 tournament.
"If Portugal hadn't qualified it would have been a blow to the 2018 bid," said Dias.
O Jogo said 400,000 Portuguese immigrants in South Africa would be eager to welcome the team next year. Around half of them have roots in Madeira, home to Portugal wing wizard Cristiano Ronaldo.
