The loved up couple - who also have children North, five, Saint, three, and 16-month-old Chicago - welcomed baby boy Psalm via surrogate on May 7, and they are said to be ''bursting with happiness'' over the new arrival.
A source told 'Entertainment Tonight': ''Kim and Kanye are bursting with happiness over Psalm. He's such an incredibly great baby, and so far, it's been an easy addition to the family...
''Kim and Kanye are both busy with their projects, but have slowed down a bit recently to spend quality time with Psalm.''
Meanwhile, it's said Kim and Kanye's older kids haven't struggled to adjust to the changes in the family, with the kids ''instantly'' falling for their new sibling.
The insider added: ''The kids instantly fell in love with him. North will always be the one in charge, but she loves her little brother.''
It was recently revealed that the tot's name is a ''reflection'' of where the couple are ''spiritually''.
It was previously reported that the couple ''mutually'' agreed on the name and that the 'Famous' rapper was ''very involved'' in the process, as a regular reader of Psalms, the religious Book from the Christian Old Testament and name of the third section of the Hebrew Bible.
A source said: ''He and Kim do exactly what every couple does, where they each bring up names and the other one gives their feedback.
''It's very traditional that way.
''Kanye would never just choose a name that Kim doesn't like, or vice versa. The names are things that they mutually agree upon.''
The insider continued: ''Psalms is the longest book in the Bible, but Kanye believes that there's a lot of wisdom in them.
''He reads the Psalms a lot. He talks about the Psalms he loves. So on that level, the baby name isn't a surprise.''
They added that Psalm is a ''reflection of where Kanye and Kim are spiritually''.
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