The pair were first romantically linked in late October.
"Kim and Pete are dating and having a great time together," the source says. "Pete is a romantic and goes out of his way to make Kim feel special. Kim thinks Pete is hysterical and he's constantly making her laugh, but they also have been connecting on a deeper level."
The pair recently spent Pete's 28th birthday in matching SKIMS pajamas, and were joined by Flavor Flav and Kim's mom, Kris Jenner. The 41-year-old reality star and Saturday Night Live comedian have also been spotted out on several dinner dates.
"They're enjoying getting to know each other better and having a lot of fun," the source adds.
Another source tells ET, "Pete and Kim are 100 percent dating and are very into each other. They are pretty much inseparable and very affectionate when they're together. They are supportive of each other's projects and are really taking an interest in what the other is passionate about. Pete has been in a great mood since him and Kim got together and he is very calm, chill and easy to get along with."
Over Halloween weekend, Kim, Pete, Kourtney Kardashian and Travis Barker all went to Knott's Scary Farm in Buena Park, California, which is where Kim was first spotted holding hands with Pete while on a roller coaster.
For more with the rumored couple, check out the video below.