Squalo become the sword emperor at a young age, after removing is left hand (dominant hand) to fight the previous emperor. He said this would help him to understand his opponent better. I might even say that Squalo is the closest thing Xanxus has to a best friend in terms of the idea that Squalo seems to know everything about Xanxus. However, I use the term loosely because when Squalo loses or is presumed dead, the first thing Xanxus does is laugh and seem as though a huge weight has been lifted off of his shoulders. This leads me to believe that Squalo's presence while necessary sometimes, is not always something that Xanxus wants to deal with. I feel like Xanxus puts up with Squalo knowing his past and secrets because Squalo isn't stupid enough to spill those secrets to just anyone.
In his youth, Squalo became the head of the Varia. He was impressed by Xanxus' presence. In flashbacks he admits that the sheer force of Xanxus' presence was enough to intimidate him and make him want to follow Xanxus. During this time, Squalo makes a promise to Xanxus that he will not cut his hair until Xanxus' plan comes into fruition. He insists that Xanxus make the same promise, but Xanxus declines with an annoyed look on his face. Squalo decides to grow out his hair anyways, and his long hair in present and future times shows his willingness and support to his boss. This also tells me that Xanxus trusted Squalo enough with the whole "bring down the family and take over" plan. I find it interesting that for all the hell he puts Squalo through, he trusts that his abilities (and Squalo's) will be enough power to achieve his dreams. I believe that Squalo is completely loyal to Xanxus not only because of his overwhelming presence but because of Xanxus ability and will to overcome any and every obstacle that stands in his way. Despite the fact that Squalo is technically the leader of the Varia, he relies on Xanxus to be the "boss". Squalo serves as the tactical leader for the Varia, but defaults to Xanxus' whims.
So, while Squalo is the head of the Varia in name, he serves as the person that gives orders and missions. He is, for all purposes, Xaxnus' right hand man. Squalo is also the only person that seems to know every one of Xanxus' secrets, including the fact that Xanxus is adopted. It is Squalo that relates this information to Tsuna and the others during the ring battles. He accompanied Xanxus in his battle with Timoteo and overheard the conversation between the two men in which Xanxus states that he's adopted. Despite this, Squalo chooses to follow Xanxus. He still follows him into battle to gain the Vongola rings, and he is still loyal to the point of stupidity in the ten years later arc. When Xanxus will not put up with Tsuna, Squalo takes over as the leader of the Varia and makes appearances on behalf of the family.
That's not to say that Squalo always enjoys his life working under Xanxus. His boss is extremely stubborn and childish. When Xanxus has had enough he does what pleases him, much too poor Squalo's dismay. Squalo continues to serve Xanxus, despite their otherwise abusive relationship. I can't fathom if it's out of respect. Squalo also has no issue yelling at Xanxus, calling him stupid, useless, or lazy. While he respects his boss' ability to fight and dominate everything, Squalo is often annoyed and frustrated with the way Xanxus actually behaves. I struggle with the idea of why Squalo continues to follow Xanxus. I do know, however, that Squalo would do anything for him. And that Xanxus still values his peace and quiet over everything else, including henchmen that talk way too much.
Yet, Squalo puts up with the abuse (hair pulling, yelling, bad mouthing, laughing at injuries, rocks and coffee throwing) and serves Xanxus willingly. I think that there's something to say for Xanxus' strength in terms of Squalo following him because Squalo is perfectly capable of leading on his own. He is the highest ranked swordsman in the world. He shares that title with one of Tsuna's boys. But, my idea is that despite all of his jerkiness, there is something compelling and drawing about Xanxus. Squalo knows that Xanxus will never be the boss of the Vongola family. He knows that his promise to grow out his hair and never cut it until Xanxus' dream comes true is a ridiculous promise, but he still keeps it. There's something to be said for that. Insanity, maybe, though I doubt that Squalo believes things will change.