Slim's overall demeanor causes George to trust him. Consider Steinbeck's opening description of Slim, something that must have resonated with George when he first saw the skinner:
There was a gravity in his manner and a quiet so profound that all talk stopped when he spoke. His authority was so great that his word was taken on any subject, be it politics of love.
This is the image that George has of Slim when he first enters the bunkhouse. When Slim meets George's acquaintance, George is taken aback with Slim's assessment of how people no longer travel with one another, something that reflect Slim's astute powers of observation. Through this initial interaction, George begins to realize the ultimate power that Slim has, something that helps to make him trust the skinner.
When Slim gives Lennie one of his puppies, George's trust is further cemented. It is from this point that George begins to confide in Slim. Steinbeck describes this as taking on the tone of a "confessional" with Slim operating as a type of priest for George. When George starts to talk about why he and Lennie lost their jobs in Weed, he stops for a moment to ask if Slim would say anything, and then George corrects himself with the reassuring, "Nah, of course you wouldn't." It is at this point where George trusts Slim. For so long in his travels with Lennie, George has had to be the source of all decision making. He had to be "the brains" of the operation for so long. It is only when he meets Slim that George recognizes that Slim is not out to cheat him or is he out to betray him. It is for this reason that George ends up trusting Slim, something that is evident at the end when it is Slim that ends up comforting and reassuring George after having to do what he did.