Karibu! (This means "Welcome!" and is used to greet someone arriving)
You can also say:
Nimefurahi kukukaribisha! (This means "I'm happy to welcome you!")
To make it more personal, you could say:
Karibu sana! (This means "Welcome very much!")
Karibu nyumbani! (This means "Welcome home!")
These phrases are used to welcome someone, and they convey a similar sentiment to "welcome me."