Celtic were crowned champions as Aberdeen failed to beat Dundee United at Tannadice on Saturday.
Irvine was part of the last Dons side to finish runners-up, all the way back in 1994.
And with Graeme Shinnie already secured as a summer arrival, Irvine believes next year's squad can prove a match for Ronny Deila's men once more.
He said: "Next season I think it is well set up. Between the management and the board it is looking positive, everything is set for Aberdeen to be more successful season after season.
"The signs are good to build on this season. Aberdeen are looking ahead and they are not just resting on their laurels.
"They've added two good players (Kenny McLean and Graeme Shinnie) to the team and maybe more and that can only be good for fans.
"It's fantastic that Aberdeen are winning every week and long may it continue.
"They've got Celtic to try and overcome to finish first, whether that be this season or next season and that is their challenge but the signs are good now and for the seasons ahead."
Source: STV