Learn Spanish (Latin America): Vengo enseguida.

In Spanish, it is very common to use the present tense to talk about actions in the immediate future, especially with verbs of motion. Saying Vengo enseguida (literally I come immediately) feels much more immediate and certain than using the future tense.

Why use vengo (I come) instead of a verb like volver (to return)?

Both work perfectly! You will hear both Vengo enseguida and Vuelvo enseguida to mean I'll be right back. Using venir in this context focuses on your arrival back to the current location. Another extremely common and casual way to say this is simply Ya vengo.

Could I say Voy enseguida instead?

That changes the meaning! Voy enseguida means I am going right away or I am on my way. You would use that when someone calls you and you are heading to where they are. You use Vengo enseguida when you are briefly leaving your current spot but promising the people there that you will return.