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".
"If Portugal hadn't qualified it would have been a blow to the 2018 bid," said Dias.
