ヨーロッパに行っていたルームメイトが昨日帰ってきた。って英語でなんて言うの？

If your room mate was travelling around Europe and came back yesterday, you can explain that as indicated above.

We can use the words "arrive" or "come back" for when someone returned back to a place where they started from.

Arrived
My roommate arrived from his travels to Europe yesterday!

Came back
Yesterday, my roommate came back from his travels to Europe!

Returned
My roommate returned yesterday from his vacation in Europe!

"My roommate arrived back home yesterday from travelling around Europe"
you're able to mix up and adapt the sentence using different adverbs.
"My roommate arrived back home yesterday from travelling around Europe"
"My roommate came back home yesterday from travelling around Europe"
"My roommate arrived returned home yesterday from travelling around Europe"

If you come back from somewhere then you are said to 'return' or to 'come back'
Someone you share your flat or house with is called your 'roommate'
yesterday means the day before today

My roommate left to travel Europe and came back yesterday.

This answer is as simple as it seems. There is no room for confusion, because you are saying that the person who left, was your roommate. You are also saying where they were, what they were doing there and exactly when they arrived home.

Yesterday, my roommate returned from his/her trip to Europe.

The same as the first answer, this sentence has the same meaning. If you return from somewhere, you come back. So again, you are confirming that your roommate came back from a European trip the previous day.

"has Returned" is a more formal way of speaking.
"is back" is a more causal way of speaking.