Feline pheronomes are what you want. In USA, the brand name is Feliway. It comes as a diffuser and as a spray. Most folks do not find the diffuser helpful at all, so get the spray.

This can NOT be sprayed directly on the cat. What you can do is make a fabric sleeve for a cat collar and spray the fabric. Then replace the collar around the neck, and the cat now takes the calming scent every place with him / her. (Thanks to Candace for this tip). I've never actually done this, but I have read about it from so many folks both on here and on a cat forum.

Cat introductions generally take a few weeks. So plan on keeping them separated for some time. If you 'mess up,' and put them together too soon, it is MUCH harder to correct things. It can take over 2 years to get 2 cats adjusted to living together if you mess up and are trying to back up and reintroduce them.