George Hirst opened the scoring inside the first minute, Jaden Philogene doubled the lead eight minutes later, and substitute Kasey McAteer put the result beyond any doubt with a third goal five minutes from time. The win was enough to confirm second place behind champions Coventry City, managed by Frank Lampard, who ended the campaign on 95 points.
For Kieran McKenna, the result completed a third promotion in four and a half years in charge of the Suffolk club — a record that now stands as one of the most impressive in English football management.
"It's probably been the hardest one, if I'm honest," said McKenna. "It means an awful lot. I know how hard we've had to work to turn it around. As a club we had such a climb and a steep fall. We've had to rebuild this team under difficult circumstances and we deserve to be where we are today."
He was careful to stay present rather than project ahead.
"I am going to enjoy this one. I'm not going to start thinking about the Premier League today."
Captain Dara O'Shea reflected the relief felt across the squad.
"It means everything. This is what we set out to do at the start of the season. I don't think anyone wanted us to do it. Everyone had their say. We had to walk the walk and we have done it."
Millwall, who defeated Oxford United 2-0 on the final day, finished third but were unable to catch Ipswich. Middlesbrough, who needed a large win to leapfrog them into the automatic places, were held to a 2-2 draw by Wrexham — a result that also ended the Welsh club's hopes of a play-off place on a dramatic afternoon.
The Championship play-offs will feature Millwall against Hull City and Southampton against Middlesbrough, with the final at Wembley on 23 May.
At the other end of the table, Sheffield Wednesday won their second game of the season — and first at home — in a 2-1 defeat of West Bromwich Albion at a jubilant Hillsborough. The result coincided with the announcement of a takeover that saved the club from dissolution. Wednesday had been deducted 12 points after entering administration in October, leaving them on zero points for the campaign. Oxford United and Leicester City also drop into League One next season.