Dr. Strange made a deal with Dormammu: he would break the time loop he trapped himself and Dormammu in, in exchange Dormammu has to leave earth alone and take his zealots with him.

Why would a powerful (and evil) being like Dormammu honor his part of the deal? What is there to stop him from just going "Psych! I'm taking earth now, nomnomnom" after Dr. Strange broke the time loop? Seems awfully nice for such a twisted creature.

Dormammu got tired of that time loop Dr. Strange created.

If he didn't keep his promise, it's a matter of time Dr. Strange will again bind him in the loop. Remember Strange still has the Time Stone. Dormammu was exhausted so he couldn't risk to get in the time loop again.

In the time loop, he wasn't able to figure it out how he kept coming back after dying so many times. So, it wasn't wise to break the promise until he finds a way to break Strange's magic.

Because he is man of his word and have moral code like his comics counterpart Strange Tales No. 127:

STRANGE: He is evil, true…but only by our human standards. According to his own lights, he has his own moral code!

Taken from similar question from sister-site.

Creatures that exist outside of time "proceed" differently than we do

Dormammu exists outside of time, so his way of thinking and making decisions must be different from ours. The closest parallels in our world (so to speak) are angels and fallen angels, and you might not be surprised to know that some major theologians have weighed in on this topic. While we mortals have a discursive rationality, proceeding from one thought to the next in succession, angels are said to have an intuitive rationality, perceiving and deciding everything they're ever going to perceive and decide simultaneously, once and for all. Or at least, because they are outside of time, so it would appear to those of us bound by time. Incidentally this is why we know the devils won't change their minds about their rebellion against Heaven... they don't reason step-by-step the way we do.

In Dr. Strange, Dormammu doesn't really proceed step by step through his plan to dominate the multiverse. His actions may appear sequential to us, because we perceive things unfolding in time. But in fact from Dormammu's perspective his entire rise and (hopefully) fall is seen in one instant. So here's the point: when Dormammu decided to take Strange's deal, as soon as Strange released him from the trap, that decision was "locked in" as it were, part of the makeup of Dormammu's timeless mind. He would not be able to "change his mind" (nor would such a double-cross likely even occur to him as a possibility). He's just not made that way.