Yes, you can put them together. There are different ways of accomplishing this, from the LLC buying the other company to you giving the assets of your company to the LLC as part of your buy-in for the LLC.
There could be some issues with payroll, unemployment accounts, workers' comp, etc. that you will need to work out whatever way you go with. Because of that, it will probably be helpful to talk to a business attorney to make sure you make the transition properly. He or she can also make sure that your LLC is set up correctly and that you and the other owner are protected from liability as much as possible.
If you have additional questions, feel free to contact me.