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 the topic of the angelic intellect. 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. Being pulled into a time loop must have been extremely disorienting for Dormammu. During that segment of his existence, Dormammu could not "see" the consequences of his attempted actions. Dormammu would not have any experience in planning or strategizing because he had always perceived his choices and their outcomes simultaneously. This seems to me to make it unlikely that Dormammu would have the cunning to plan a deception. Remember, Dormammu would never before even have had the occasion to use imagination.

So here's the main 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"... He's just not made that way. Moreover, he probably wouldn't have planned a double-cross during the time loop, because he neither had the experience nor the developed imagination to make such a plan while blind to the future.