Dortmund, with two goals each from Jakub Blaszczykowski and Robert Lewandowski, finished on 81 points, eight ahead of
"My team showed character and did not allow any doubts to rise," a beaming Dortmund coach Juergen Klopp told reporters after his team's 28th successive game without defeat, another Bundesliga best.
"Something extraordinary happened today and that is that we got 81 points, something that is unlikely to be equalled by another team any time soon," said Klopp.
Apart from the sold-out stadium another 12,000 fans had watched the game in a public viewing area nearby.
It was a completely different atmosphere in Cologne with the team's fifth relegation coming in the last game for the club's favourite striker Lukas Podolski who is joining Arsenal.
Angry fans lit fires in the stands and briefly stormed the pitch after the final whistle before police pushed them back.
"This is a bitter and dark day for us," said Cologne coach Frank Schaefer, who took over on an interim basis only weeks ago after the sacking of Stale Solbakken.
"It was a brutally unnecessary relegation. Not having been able to avoid the drop despite this strength, these fans, this power is bitter," said Schaefer, who said he would not remain head coach next season.
Hertha's Anis Ben-Hatira scored twice in their 3-1 win over 10-man
"The tension was more than 100 percent with my players but we grabbed this relegation playoff spot with passion and determination," said Hertha coach Otto Rehhagel, who took over late in the season to save the club from the drop.
Gladbach's top scorer Marco Reus was on target in his last appearance for the club before joining Dortmund.
A sea of yellow-black flags in Europe's biggest standing tribune welcomed Dortmund players on a rainy afternoon but as far as the 80,000 fans in the stadium were concerned the sun was shining brightly on Dortmund.
Blaszczykowski kicked off the celebrations with a fifth- minute goal before Poland team mate Lewandowski struck twice to take his tally to 22 goals.
Blaszczykowski completed the rout six minutes before the break to make sure captain Sebastian Kehl lifted the trophy into the steel gray sky amid a shower of yellow confetti.
Dortmund can now prepare for the German Cup final on May 12 and a possible domestic double.