Deschamps expects 'big things' from France
France had to overcome a two-goal deficit after losing 2-0 in the first leg in Kiev on Friday, and they did just that with a superb 3-0 triumph at the Stade de France on Tuesday.
The hosts attacked right from the off and deservedly headed into half-time with the tie level on aggregate, after goals from Mamadou Sakho and Karim Benzema.
Ukraine were further hindered in the 47th minute when Yevhen Khacheridi was sent off for a second bookable offence when he chopped down Franck Ribery.
The numerical advantage paid dividends for France with 18 minutes remaining as Sakho's effort found its way to goal via a touch off Oleh Husyev.
And Deschamps hailed an "important" reversal in fortunes, insisting that he always had faith in his side's battling qualities to reach the finals in Brazil.
"This is the magic of football," he told TF1. "Four days ago, we were in a bad position but the players were fantastic tonight.
"I didn't have doubts but we played a huge match and this qualification is very important for French football. It's a bit of a tradition that when French teams have their backs against the wall they perform and we had a lot of heart and determination.
"Now we've qualified, we're capable of some great things."
Bayern Munich talisman Ribery also hailed the country's achievement and was delighted with the application of the squad.
"It's great, it's beautiful," he said. "We are very, very happy. Now we can go back to our clubs with joy and start to think about Brazil.
"It would have been difficult not to see France in Brazil. We went to get the qualification. We won, we showed good character."