John Gill Commentary Matthew 8:13

"And Jesus said unto the centurion, Go thy way; as thou hast believed, [so] be it done unto thee. And the servant was healed in that hour." — Matthew 8:13 (ASV)

And Jesus said to the centurion
Christ having finished the digression, returns an answer to the centurion, agreeably to his desire, saying to him,

go your way ;
not as displeased with him, but as granting his request: for it follows,

and as you have believed, so be it done to you .
As he had faith to believe, that Christ could cure his servant by a word speaking, it was done accordingly. Christ by his almighty "fiat" said, let him be healed, and he was healed: just as God in the creation said, "let there be light, and there was light".

He does not say according to your prayer, or according to your righteousness, and goodness, but according to your faith: and it is further to be observed, that this cure was done, not so much for the sake of the servant, as his master; and therefore Christ says, "be it done to you"; let him be healed for your sake, and restored to you, to your use, profit, and advantage.

And his servant was healed in the selfsame hour ,
at the very exact time, even in that moment. Some copies add, "and when the centurion returned to his house, in the selfsame hour he found his servant healed"; which the Ethiopic version has, and it agrees with (Luke 7:10) .