From various meforshim (from memory as I do not have the sources available) such as Nechama Leibowitz, Rabbi J. H. Hertz, Rabbi Wein, Rabbi HirchHirsch.
Given that the first mention of watering the garden was from the mist, it could have been that the heavy moisture in the atmosphere before the flood did not allow for a rainbow. During the flood, all the water in the atmosphere condensed leaving the atmosphere the way it is now (which allowed a rainbow to occur). Since Noach had been shut up in the ark the whole time, this was the first time that he could have seen one. Hashem then told him the meaning of the rainbow, especially tied to the fact that all the water in the atmosphere had flooded the Earth.
Rainbows could have existed before, but this time it was being given a religious and symbolic meaning. Once it was given this meaning, seeing it would bring to mind what had happened and what Hashem wanted people to remember. @MichaBerger points out that htisthis is the view of the Ramban.
As Rav Hirsch says at Noach 9:13
It is by no means necessary to assume that there had been no rainbow and to place it in connection with the atmospheric changes which occurred after the Flood. Just as Hashem showed Avraham the starry heavens ... My bow, I have long ago placed it in the clouds, henceforth it shall serve as a sign of the covenant between Me and you.