The Portuguese failed to deliver a European trophy in his first spell at Chelsea but the former assistant manager believes domestic success should remain his priority
The Portuguese lifted the English title twice in three seasons in his first spell at Stamford Bridge but could not guide the Blues to glory in Europe.
Wilkins, however, insists that domestic success should remain Mourinho's priority following his much-anticipated appointment on Monday.
"Mourinho's main aim will be to wrestle back the Premier League," the former Blues assistant manager told Sky Sports. "I think Sir Alex Ferguson's main aim was to wrestle back the Premier League from Manchester City and he did so.
"Finishing third or fourth is no good to Chelsea - they need to be finishing up there and fighting for the Premier League.
"I know the Champions League is a great trophy but the best trophy you can win is your domestic trophy. That shows consistency and a level of performance over 38 games. Anything else becomes a bit of a bonus."
Wilkins added that Mourinho can fill the void left by the retiring Sir Alex Ferguson as one of the Premier League's leading personalities.
"I'm thrilled," he continued. "Having lost Sir Alex Ferguson, who has been unbelievably good, from our game it's nice that we've got another fantastic personality coming back into our game. It's good for Chelsea and the Premier League as well.
"The people at Chelsea absolutely adore the guy and the supporters love him to bits. He wants to be loved - so we read - and he's going back to the best place for him.
"I'm sure that with the players that they bought last year - now they've got another year's experience in the Premier League - that Chelsea will be one of the top teams once again next year.
"They [Abramovich and Mourinho] fell out because of principal - Jose wanted it one way and Mr Abramovich wanted it to go another way.
"I would assume that they've spoken on numerous occasions to sort out their differences and have come to a very happy ending."
Chelsea left-back Ryan Bertrand, meanwhile, expressed his excitement at the prospect of working under Mourinho next season.
"This is what we've been waiting for!" he tweeted. "welcome back #mourinho excited for the new season already."
"Great to have confirmation that The Special One returns to The Premier League," former Liverpool and Manchester United striker Michael Owen added. "What a season we have in store."