The six-time German champions, who won the European Cup in 1983, are the only team to have played in every single Bundesliga season since the league's inauguration in 1963, earning them the nickname "dinosaur".
At Hamburg - who had survived the relegation play-offs in 2014 and 2015 - Gladbach fans mocked their counterparts by unfurling their own clock which ticked down towards their opponents' impending demotion, and as the game entered stoppage-time a number of home fans hurled flares towards the pitch.
After flirting with relegation in recent seasons, Hamburg needed a win and a favor from already relegated Cologne against Wolfsburg to maintain hope of another escape.
"This is an extremely painful moment for the entire Hamburg SV", said club President Bernd Hoffmann.
"The diamond [club logo] and us as a club are strong despite this current moment and we will in the future again reflect that strength".
There were troubling scenes in the 90th minute of the match as police were forced to storm onto the pitch after one section of the home support let off a series of flares and fireworks, which engulfed the stand behind the goal in smoke, delaying the end of the game.More news: Klopp: Liverpool players could be remembered for 500 years with European glory
Minutes later, Robin Knoche headed in Wolfsburg's third, and when Josip Brekalo added a fourth in stoppage time, Hamburg's fight was over.
Play resumed 15 minutes later, if only for the referee to blow the final whistle and confirm Hamburg's relegation.
Hamburg actually beat Gladbach 2-1 at Volksparkstadion, with goals coming from Aaron Hunt and Lewis Holtby.
With the stadium clock marking the club's record stay in the Bundesliga and showing 54 years and 260 days, fans stayed in their seats and with tears in their eyes gave the players their last Bundesliga cheer.
Champions Bayern Munich saw their five-game winning run brought to an end as they were thrashed 4-1 at the Alianz Arena by Stuttgart.
Following Leipzig's 6-2 away win against Hertha Berlin, they pick up a Europa League qualifying ticket.