Yes, you may sponsor him. Whether he can become legal depends upon how he entered the country and if he has any "strikes" against him that would prevent the process from going forward (e.g., certain crimes either in his home country or here). And, even if he did enter illegally or he has a "strike" against him, there are waivers for certain situations available, especially if you have children together and they were born in the United States. Because of the current hostility towards illegal aliens, if he is able to become legal, you really need to do it asap. Additionally, the law may change at any time, making it difficult or impossible to become legal. You want to become legal now, if you are able.