Jose Mourinho was reunited with the 29-year-old after he signed him from Chelsea for £40m.
Matic was keen to move to Old Trafford following the arrival of Tiemoue Bakayoko at Stamford Bridge.
And while his importance was not fully appreciated at Chelsea, United have seen the difference immediately.
The holding midfielder has allowed Paul Pogba to contribute more in attack.
And Manchester United have scored eight goals in their opening two Premier League games as a result.
Romelu Lukaku was also acknowledged by Ibrahimovic, but the striker feels Matic is vital.
"I think the signing of Matic [is crucial]," Ibrahimovic told ESPN FC.
"He brings a stability to the team that it didn't have last year.
"And I think Lukaku was a quality signing, like physical signing of force, but the important one is Matic.
“He brings stability to the whole team and that is what the team needs, and to have a player who is consistent at the top level.
"I also think this season will be the season of [Henrikh] Mkhitaryan because he has opened fantastic.
"I think people underestimate him because he doesn't have the name like the other ones in the world.
“This may be because he comes from a small country like he comes from [Armenia] but this year he will get the credit he deserves and show the quality that he is, my bet is on Mkhitaryan.
“Or if he don't provide me [goals] he will not play... I am joking!"
Matic won two Premier League titles with Chelsea, and following Ibrahimovic’s official return yesterday, top spot is being targeted by Mourinho’s men.
