Heidenheim were also relegated on Saturday (Sunday AEST) while Wolfsburg grabbed the last chance for survival by beating St. Pauli 3-1.
That win sent the home team down and qualifies Wolfsburg for a playoff in which they will be favoured against the third-place finisher from the second division, to decide who play in the top division next season.
Ahead of the clash, Irvine spoke of how hard they needed to work and his love for the opportunity.
"From an individual point of view and for everything I have invested in this team and with this club over the years, to have the chance to compete at this level is all I have ever dreamed of," he said.
"I wanted the chance to compete week in, week out at the very highest level and that is what the Bundesliga is.
"It is one of the top two or three leagues in the world and what it takes to get here and stay here is monumental levels of physical and mental investment."
Heidenheim, who had been level with Wolfsburg and St. Pauli going into the final round, needed a win at home against Mainz to keep alive their hopes, but slumped to a 2-0 loss.
The last two are automatically relegated to the second division.
Both demoted teams were given shows of support and appreciation by their fans despite their disappointment.
St. Pauli's defeat extended their winless run to 10 games and left them bottom of the table, but the fans still held their scarves aloft in solidarity.
It was similar in Heidenheim, where the team's coach of nearly 19 years, Frank Schmidt, expressed how grateful he was.
"To be relegated like this, and yet you go over to our fans and flags are being waved, you really have to let that sink in," he said.
"It's something you don't see very often. I wish society, us here in Germany, had the kind of solidarity that we have within this club."
Stuttgart held on for the last Champions League qualification spot despite conceding two late goals in a 2-2 draw at Eintracht Frankfurt, denying Hoffenheim and Bayer Leverkusen their chance.
Both rivals were hoping for a favour from Frankfurt but they failed to win in any case. Hoffenheim lost at Borussia Mönchengladbach 4-0 and Leverkusen could only draw with Hamburger SV 1-1.
Harry Kane scored a hat trick to take his season tally to 36 Bundesliga goals in league champion Bayern Munich 's 5-1 win at home over Cologne.
Leon Goretzka started his last Bundesliga game with Bayern, who were presented with the league trophy after the game.
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