Be aware that the stray will have been exposed to things that your indoor cat has not; that being said, feed them separately with their own food and water dishes, and separate litter areas, because most parasites and diseases are transmitted via these sources. Make sure to vaccinate both for the new family circle and deworm as soon as possible. I am not a proponent of flea dips, shampoos or collars because of the potential of harm to the pet, but it is an issue you will need to address because the stray will potentially have ticks, lice, or fleas that will move into your environment as well.
This may sound strange, but it may be a good idea to keep the new kitty in the bathroom or another room with no carpet or soft furniture for a few days, and put salt an/or diatomaceous earth around the perimeter of the room, and if possible to dust the cats bedding with the D.E. as well. Groom the new cat with a brush or comb in the sink, tub, or shower, and look for signs of mites, fleas, ticks, etc. For the few days you have them separate, feed both cats the same diet, providing probiotics in their food and providing colloidal silver in their water. If you put flea and tick collars on them, don't leave them on unattended, as they may chew on them or strangle themselves with it if they are not used to one or if they get caught on something.
When you are confident in a few days, slowly introduce them, making sure not to neglect or ignore either because they both have emotional attachment and could exhibit behavior issues. Additionally, if you do find signs of parasites, it is said that you can dust a pet with diatomaceous earth, avoiding breathing in the dust; this will kill off mites, larva, lice, ticks, and such.
Suggestions listed, research for yourself first; hope this is helpful.