What is correct? It depends on the context of time (past, present, future) based on what you have said/written before this sentence. What is correct is what temporal perspective you want to place your narrating relative to these chain of events.
What you chose: To place you after everything happened with both verbs in the past tense.
You are talking about a chain (order matters) of events (time related) within the same sentence. So playing with the tense of your chosen verbs "leave" and "receive" changes the meaning of when (time) you are talking/writing this relative to these two events within the chain (past, present or future). The listener/reader knows there is a logical order to the events such that you couldn't use the combination of past tense for "leave" and future tense for "receive". For example, if you use the past tense of "receive" relative to using the future tense of "leave", you have placed the time that you are talking/writing as coming between the two chained events and not after the entire chain of events like you chose.
Example of you the writer placing the reader in time between the two events by using the future tense of leave and the past tense of receive:
A BBC special news team will leave (future tense: this event hasn't happened yet) for Cairo immediately now that we have received news of the earthquake.